Analysis in Theory and Applications
type: channel
description: Analysis in Theory and Applications (ATA), used to have the title Approximation Theory and its Applications (from 1984 to 2002), publishes research results in broad areas of approximation including Dynamic Systems, Geometric Analysis, Harmonic Analysis, Numerical Approximation, Signal Analysis, Special Functions, Differential Equations, Wavelets, and Approximation Theory, as well as their applications. The journal is supervised by Office of Education of Jiangsu Province and sponsored by Nanjing University.
publisher: Global Science Press
language: en
publication name: Analysis in Theory and Applications
issn: 1672-4070
items: Functional-Vector Spaces $\mathscr{L}^2 (X,σ(X),\mu_t)$ with Scaled-Hyperbolic-Valued Probabilities $\mu_t$
items: On Nodal Solutions with A Prescribed Number of Nodes for a Schrödinger-Poisson system
items: Regularity Criteria of the 3D Double-Diffusive Convection System
items: Existence and Regularity for Minimizers of Some Noncoercive Integral Functionals
items: Generalized Hermite-Hadamard Inequalities for Subadditive Functions via Katugampola Fractional Integrals
items: Weak Solutions of the Two-Dimensional Incompressible Inhomogeneous Navier-Stokes Equations in the Presence of Variable Odd Viscosity
items: On the Spectrality of a Class of Moran Measures
items: Existence of Positive Solutions for Kirchhoff Type Problem with Singular and Logarithmic Nonlinearity
items: The Characterizations of the Hardy Space Associated with Schrödinger Operators via Square Functions on Heisenberg Groups
items: Author Index to Volume 41
items: Preface: Special Issue Dedicated to the Memory of Prof. Donggao Deng’s 90th Birthday (Part II)
items: Preface: Special Issue Dedicated to the Memory of Prof. Donggao Deng’s 90th Birthday (Part I)
items: Bilinear Fractional Integral Operators
items: $L^p$ → $L^q$ Estimates for Stein’s Spherical Maximal Operators
items: Weak Boundedness for Commutators of $n$-Dimensional Hardy-Type Operators on Mixed Herz Spaces
items: Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions
items: Long Time Behavior of the Modified One-Dimensional Derivative Schrödinger Equation
items: Matrix Weights, Maximal Operators, Calderón–Zygmund Operators, and Besov–Triebel–Lizorkin-Type Spaces — A Survey
items: δ-Universal Taylor Series
items: A Signal Separation Method Based on Instantaneous Frequency Embedded Continuous Wavelet Transform and Short-Time Fourier Transform
items: Singular Integral and Local Hardy Spaces in Dunkl Setting
items: Weighted Boundedness of Toeplitz Type Operator Associated to General Singular Integral Operator Satisfying a Variant of Hörmander’s Condition
items: Variable Exponent Central Morrey Estimates for Multilinear Bochner-Riesz Operators
items: Liouville Type Theorems for a Class of General Parabolic Hessian Quotient Type Equations
items: A Rigidity Result for the Schiffer Conjecture on Domain with a Hole
items: Estimates for Parabolic Schrödinger Operators with Certain Nonnegative Potentials
items: Separation of Sequences and Multipliers in the Space of Tempered Distributions
items: Double Cosine and Cosine-Sine Fourier Transforms and Generalized Lipschitz Classes in Uniform Metric
items: On Noveley Inequalities for Convex Stochastic Processes on Time Scale Utilizing Quantum Operators
items: Multiplicity of Solutions for an Integro-Differential Equation with Trudinger-Moser Subcritical or Critical Nonlinearities

Functional-Vector Spaces $\mathscr{L}^2 (X,σ(X),\mu_t)$ with Scaled-Hyperbolic-Valued Probabilities $\mu_t$
type: item
description: In this paper, we construct a natural $\mathbb{D}_t$-valued-functional-vector space $$\mathscr{L}^2(X,σ(X),\mu_t)$$on a measurable space $(X,σ(X))$ up to a $\mathbb{D}_t$-valued probability $\mu_t,$ where $\mathbb{D}_t$ is the $t$-scaled hyperbolic numbers for an arbitrarily fixed scale $t ∈ \mathbb{R}.$ We show that this vector space $\mathscr{L}^2 (X,σ(X),\mu_t)$ is Banach space over the real field $\mathbb{R},$ equipped with symmetric $\mathbb{D}_t$-valued-positive $\mathbb{R}$-bilinear form for any $t ∈ R.$ As application, we consider multiplication operators acting on $\mathscr{L}^2 (X,σ(X),\mu_t).$
subject: Articles
  topic: section
subject: Scaled hypercomplex rings
  topic: keywords
subject: scaled hypercomplex monoids
  topic: keywords
subject: scaled hyperbolic numbers
  topic: keywords
creator: Daniel Alpay
creator: Ilwoo Cho
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-26
publication date: 2026-03-26
doi: 10.4208//ata.OA-2025-0050

On Nodal Solutions with A Prescribed Number of Nodes for a Schrödinger-Poisson system
type: item
description: We study a class of Schrödinger-Poisson problems involving the nonlinearity $f(x)|u|^{p-2}u$ $(2 < p < 4)$ in $\mathbb{R}^3.$ Such problems cannot be studied directly by applying the general Nehari manifold, because $(PS)$ sequence may not be bounded. In this paper, by developing some useful analytical techniques and introducing a novel definition of the Nehari manifold for the auxiliary system of equations, we resolve an open question posed in [S. Kim and J. Seok, Commun. Contemp. Math., 14 (2012)] of whether there exists a sign-changing solution $u_k^\lambda$ changing signs exactly $k$ times to the problem above for the remaining range $2 < p < 4$. Furthermore, the energy of $u_k^\lambda$ is strictly increasing in $k,$ as well as some asymptotic behaviors of $u_k^\lambda$ are obtained.
subject: Articles
  topic: section
subject: Nonlinear Schrödinger-Poisson equations
  topic: keywords
subject: variational methods
  topic: keywords
subject: nodal solutions
  topic: keywords
subject: Nehari manifolds
  topic: keywords
creator: Qian Wang
creator: Haining Fan
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2025-0045

Regularity Criteria of the 3D Double-Diffusive Convection System
type: item
description: In this paper, we study the 3D double-diffusive convection system. Using energy methods and Littlewood-Paley decomposition theory, we establish regularity criteria for the system in Lorentz spaces and sum spaces, respectively.
subject: Articles
  topic: section
subject: Double-diffusive convection system
  topic: keywords
subject: regularity criteria
  topic: keywords
subject: strong solution
  topic: keywords
creator: Bo Xu
creator: Jiang Zhou
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2025-0033

Existence and Regularity for Minimizers of Some Noncoercive Integral Functionals
type: item
description: This paper deals with minimizers for noncoercive integral functional of the type $\mathcal{J}(v) = \int_{\Omega} a(x)|\nabla v(x)|^p dx - \int_{\Omega} f(x)v(x)dx,\quad v\in W_0^{1,p}(\Omega), $ with $1 < p < n, 0 < a(x) \leq \beta, a.e. \Omega$ and $\frac{1}{a(x)}$ and $f(x)$ belong to some Lebesgue or Marcinkiewicz spaces. It is shown by Weierstrass Theorem that such a functional has a minimizer in a larger space $W_0^{1,q}(\Omega)$ for an appropriate exponent $1 < q < p$. Some regularity properties are given by using Stampacchia Lemma. This paper also considers regularizing effect of an interplay between the coefficient of zero order term and the datum in noncoercive integral functional of the type $ \mathcal{I}(v)=\int_{\Omega} a(x)|\nabla v(x)|^p dx + \int_{\Omega} b(x)|v(x)|^p dx - \int_{\Omega} f(x)v(x)dx,\quad v\in W_0^{1,p}(\Omega). $ It is shown that, even if $0 < b(x)$ and $f(x)$ belong only to $L^1(\Omega)$, the interplay $ |f(x)| \leq 2Q b(x) $ implies the existence of a minimizer $u\in W_0^{1,q}(\Omega)$ satisfying $|u| \leq Q$.
subject: Articles
  topic: section
subject: Regularity
  topic: keywords
subject: noncoercive integral functional
  topic: keywords
subject: minimizer
  topic: keywords
subject: Weierstrass Theorem
  topic: keywords
subject: Stampacchia Lemma
  topic: keywords
creator: Hongya Gao
creator: Ruiqi Lv
creator: Qianqian Liu
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2025-0017

Generalized Hermite-Hadamard Inequalities for Subadditive Functions via Katugampola Fractional Integrals
type: item
description: This investigation provides a comprehensive derivation of integral inequalities for subadditive functions within the framework of Katugampola fractional integrals. Using Katugampola fractional integrals, this study extends Hermite-Hadamard inequalities to subadditive functions. It establishes and investigates several variations of these inequalities and fractional integral inequalities for the product of two subadditive functions using Katugampola fractional integrals. Furthermore, we demonstrate that the inequalities presented in this research generalize the previously established inequalities for convex functions.
subject: Articles
  topic: section
subject: Subadditive function
  topic: keywords
subject: Hermite–Hadamard inequalities
  topic: keywords
subject: Katugampola fractional integral
  topic: keywords
subject: convex functions
  topic: keywords
creator: Asia Shehzadi
creator: Hüseyin Budak
creator: Wali Haider
creator: Fatih Hezenci
creator: Haibo Chen
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2025-0013

Weak Solutions of the Two-Dimensional Incompressible Inhomogeneous Navier-Stokes Equations in the Presence of Variable Odd Viscosity
type: item
description: We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of weak solutions in both the evolutionary and stationary cases. Furthermore, we investigate the limit of the weak solutions as the odd viscosity coefficient converges to a constant. Lastly, we consider examples of stationary solutions for parallel, concentric and radial flows.
subject: Articles
  topic: section
subject: Odd viscosity
  topic: keywords
subject: variable viscosity
  topic: keywords
subject: weak solutions
  topic: keywords
subject: incompressible fluids
  topic: keywords
subject: Navier-Stokes equations
  topic: keywords
creator: Rebekka Zimmermann
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2024-0056

On the Spectrality of a Class of Moran Measures
type: item
description: In this paper, we study the spectrality of a class of Moran measures $\mu_{\mathcal{P},\mathcal{D}}$ on $\mathbb{R}$ generated by $\{(p_n, D_n)\}^∞_{n=1},$ where $\mathcal{P} = \{p_n\}^∞_{n=1}$ is a sequence of positive integers with $p_n > 1$ and $\mathcal{D}= \{D_n\}^∞_n=1$ is a sequence of digit sets of $\mathbb{N}$ with the cardinality #$D_n ∈ \{2, 3, N_n\}.$ We find a countable set $Λ ⊂ \mathbb{R}$ such that the set $\{e^{−2πiλx}|λ ∈ Λ\}$ is an orthonormal basis of $L^2 (\mu_{\mathcal{P},\mathcal{D}})$ under some conditions. As an application, we show that when $\mu_{\mathcal{P},\mathcal{D}}$ is absolutely continuous, $\mu_{\mathcal{P},\mathcal{D}}$ not only is a spectral measure, but also its support set tiles $\mathbb{R}$ with $\mathbb{Z}.$
subject: Articles
  topic: section
subject: Moran measures
  topic: keywords
subject: spectrality
  topic: keywords
subject: orthonormal basis
  topic: keywords
subject: Hadamard triple
  topic: keywords
creator: Yali Zheng
creator: Yingqing Xiao
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2024-0025

Existence of Positive Solutions for Kirchhoff Type Problem with Singular and Logarithmic Nonlinearity
type: item
description: In this paper, we consider the following Kirchhoff type problem with singular and logarithmic nonlinearity where $Ω ⊂ \mathbb{R}^3$ is a bounded domain with smooth boundary, $0 < γ < 1,$ $4 < p < 6,$ $λ$ is positive constant. By using variational method and the critical point theory for nonsmooth functional, we obtain the existence of two positive solutions. In particular, we propose innovative techniques to tackle the challenges arising from the sign-changing property of $u^{p−1} {\rm ln} |u|,$ which violates both the monotonicity condition and the Ambrosetti-Rabinowitz condition. Moreover, unlike the scenario where $a = 1$ and $b = 0,$ the inclusion of the nonlocal term $(\int_Ω |∇u|^2dx)∆u$ brings about extra complexities. A key issue here is the lack of weak continuity in the functional for any $v ∈ H_0^1(Ω),$ a factor that substantially complicates the proof that the limit of a $(PS)_c$ sequence corresponds to a nontrivial solution of the problem.
subject: Articles
  topic: section
subject: Kirchhoff Type equation
  topic: keywords
subject: singular
  topic: keywords
subject: logarithmic nonlinearity
  topic: keywords
subject: positive solutions
  topic: keywords
subject: variational method
  topic: keywords
creator: Deke Wu
creator: Hongmin Suo
creator: Changmu Chu
creator: Linyan Peng
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2021-0010

The Characterizations of the Hardy Space Associated with Schrödinger Operators via Square Functions on Heisenberg Groups
type: item
description: In this paper we assume that $L = −∆_{\mathbb{H}^n}+ V$ is a Schrödinger operator on the Heisenberg group $\mathbb{H}^n,$ where the nonnegative potential $V$ belongs to the reverse Hölder class $B_{Q/2}.$ We introduce the Littlewood-Paley $\mathfrak{g}$-functions, the Lusin area functions and the $\mathfrak{g}^∗_λ$-functions generated by the heat semigroup $\{e^{−tL}\}_{t>0}$ and the Poisson semigroup $\{e^{−t\sqrt{L}}\}_{t>0},$ respectively. By means of the reproducing formulas and the regularity properties of semigroups, we establish several square function characterizations of the Hardy space $H_L^1(\mathbb{H}^n)$ associated with $L.$
subject: Articles
  topic: section
subject: Schrödinger operators
  topic: keywords
subject: the Hardy space
  topic: keywords
subject: regularity properties
  topic: keywords
subject: operator semigroups
  topic: keywords
subject: square functions
  topic: keywords
creator: Zhiyong Wang
creator: Jing Yu
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-03-19
publication date: 2026-03-19
doi: 10.4208/ata.OA-2020-0028

Author Index to Volume 41
type: item
subject: Articles
  topic: section
rights: Copyright (c) 2026 Analysis in Theory and Applications
date: 2026-01-19
publication date: 2026-01-19
starting page: 479
ending page: 479

Preface: Special Issue Dedicated to the Memory of Prof. Donggao Deng’s 90th Birthday (Part II)
type: item
subject: Articles
  topic: section
creator: Ji Li
creator: Heping Liu
creator: Lizhong Peng
creator: Lixin Yan
rights: Copyright (c) 2026 Analysis in Theory and Applications
date: 2026-01-19
publication date: 2026-01-19
starting page: i
ending page: iii
doi: 10.4208/ata.2026.v42n1.preface

Preface: Special Issue Dedicated to the Memory of Prof. Donggao Deng’s 90th Birthday (Part I)
type: item
subject: Articles
  topic: section
creator: Ji Li
creator: Heping Liu
creator: Lizhong Peng
creator: Lixin Yan
rights: Copyright (c) 2026 Analysis in Theory and Applications
date: 2026-01-19
publication date: 2026-01-19
starting page: i
ending page: iii
doi: 10.4208/ata.2025.v41n4.preface

Bilinear Fractional Integral Operators
type: item
description: We study the bilinear fractional integral considered by Kenig and Stein, where linear combinations of variables with matrix coefficients are involved. Under more general settings, we give a complete characterization of the corresponding parameters for which the bilinear fractional integral is bounded from $L^{p_1}(\mathbb{R}^{n_1}) × L^{p_2}(\mathbb{R}^{n_2})$ to $L^q(\mathbb{R}^m)$.
subject: Articles
  topic: section
subject: Bilinear fractional integrals
  topic: keywords
subject: Riesz potentials
  topic: keywords
creator: Ting Chen
creator: Wenchang Sun
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 32
ending page: 61
doi: 10.4208/ata.2025.deng90.06

$L^p$ → $L^q$ Estimates for Stein’s Spherical Maximal Operators
type: item
description: In this article we consider a modification of the Stein's spherical maximal operator of complex order $\alpha$ on $\mathbb{R}^n$: $\mathfrak{M}_{[1,2]}^{\alpha} f(x) = \sup\limits_{t \in [1,2]} \left| \frac{1}{\Gamma(\alpha)} \int_{|y| \leq 1} \left( 1 - |y|^2 \right)^{\alpha - 1} f(x - ty) dy \right|.$ We show that when $n \geq 2$, suppose $\|\mathfrak{M}_{[1,2]}^{\alpha} f\|_{L^q(\mathbb{R}^n)} \leq C \|f\|_{L^p(\mathbb{R}^n)}$ holds for some $\alpha \in \mathbb{C}$, $p, q \geq 1$, then we must have that $q \geq p$ and $$\operatorname{Re} \alpha \geq \sigma_n(p, q) := \max \left\{ \frac{1}{p} - \frac{n}{q},\; \frac{n+1}{2p} - \frac{n-1}{2} \left( \frac{1}{q} + 1 \right),\; \frac{n}{p} - n + 1 \right\}.$$ Conversely, we show that $\mathfrak{M}_{[1,2]}^{\alpha}$ is bounded from $L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ provided that $q \geq p$ and $\operatorname{Re} \alpha > \sigma_2(p, q)$ for $n = 2$; and $\operatorname{Re} \alpha > \max \left\{ \sigma_n(p, q),\; 1/(2p) - (n-2)/(2q) - (n-1)/4 \right\}$ for $n > 2$. The range of $\alpha$, $p$ and $q$ is almost optimal in the case when either $n = 2$, or $\alpha = 0$, or $(p, q)$ lies in certain regions for $n > 2$.
subject: Articles
  topic: section
subject: spherical maximal operators
  topic: keywords
subject: $L^p$-improving estimates
  topic: keywords
subject: wave equation
  topic: keywords
subject: local smoothing estimates
  topic: keywords
creator: Naijia Liu
creator: Minxing Shen
creator: Liang Song
creator: Lixin Yan
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 90
ending page: 108
doi: 10.4208/ata.2025.deng90.04

Weak Boundedness for Commutators of $n$-Dimensional Hardy-Type Operators on Mixed Herz Spaces
type: item
description: In this paper, we obtain the boundedness for the commutators of $n$-dimensional Hardy-type operators from mixed Herz spaces to weak mixed Herz spaces, where the symbol functions are in the intersection of the mixed central bounded mean oscillation space $\text{CBMO}_{\vec{q'}}(\mathbb{R}^n)$ and the weak mixed central bounded mean oscillation space $W_{\vec{q}}(\mathbb{R}^n)$.
subject: Articles
  topic: section
subject: Weak mixed central bounded mean oscillation space
  topic: keywords
subject: $n$-dimensional Hardy-type operators
  topic: keywords
subject: commutator
  topic: keywords
subject: weak mixed Herz space
  topic: keywords
creator: Lei Ji
creator: Mingquan Wei
creator: Dunyan Yan
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 469
ending page: 478
doi: 10.4208/ata.2025.deng90.03

Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions
type: item
description: Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $ℓ_1$ to $ℓ_2$ norms, $(ℓ_1/ℓ_2)^2,$ has been introduced as a sparsity-prompting function, showing superior performance compared to traditional $ℓ_1$ minimization, particularly in challenging scenarios with high coherence and dynamic range. This paper explores the integration of the proximity operator of $(ℓ_1/ℓ_2)^2$ and $ℓ_1/ℓ_2$ into efficient optimization frameworks, including the Accelerated Proximal Gradient (APG) and Alternating Direction Method of Multipliers (ADMM). We rigorously analyze the convergence properties of these algorithms and demonstrate their effectiveness in compressed sensing and image restoration applications. Numerical experiments highlight the advantages of our proposed methods in terms of recovery accuracy and computational efficiency, particularly under noise and high-coherence conditions.
subject: Articles
  topic: section
subject: Sparse signal recovery
  topic: keywords
subject: compressed sensing
  topic: keywords
subject: image restoration
  topic: keywords
subject: $(\ell_1/\ell_2)^2$
  topic: keywords
subject: optimization algorithms
  topic: keywords
creator: Jianqing Jia
creator: Ashley Prater-Bennette
creator: Lixin Shen
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 62
ending page: 89
doi: 10.4208/ata.2025.deng90.02

Long Time Behavior of the Modified One-Dimensional Derivative Schrödinger Equation
type: item
description: We study the long time behavior of the modified one-dimensional deriva- tive Schrödinger equation $(D_t - F(D))u = D_x(|u|^2u)$, where $F(\xi)$ is a nonnegative second order constant coefficient elliptic symbol. For any smooth initial datum of size $\varepsilon \ll 1$, we prove that the solution is global-in-time, combining the vector fields method and a semiclassical analysis method introduced by Delort. Moreover, we present the pointwise decay estimates and the large time asymptotic formulas of the solution.
subject: Articles
  topic: section
subject: Derivative Schrödinger Equation
  topic: keywords
subject: semiclassical analysis
  topic: keywords
subject: large time asymptotics
  topic: keywords
creator: Xuan Liu
creator: Ting Zhang
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-10
publication date: 2026-01-10
doi: 10.4208/ata.OA-2025-0060

Matrix Weights, Maximal Operators, Calderón–Zygmund Operators, and Besov–Triebel–Lizorkin-Type Spaces — A Survey
type: item
description: The primary purpose of this survey is threefold. First, the authors recall some histories and present some recent developments of matrix weights, in which the authors not only improve some known results on the intrinsic properties of matrix weights, but also establish some new ones. Then the authors summarize matrix-weighted inequalities associated with various operators, such as Hardy–Littlewood-type maximal operators and Calderόn–Zygmund operators. Finally, the authors overview matrix-weighted function spaces, including matrix-weighted Sobolev, BMO, and Besov–Triebel–Lizorkin-type spaces. Several open questions on these subjects are also presented.
subject: Articles
  topic: section
subject: Sobolev space
  topic: keywords
subject: BMO
  topic: keywords
subject: Besov–Triebel–Lizorkin-type space
  topic: keywords
subject: matrix weight
  topic: keywords
subject: Hardy–Littlewood maximal operator
  topic: keywords
subject: Calderón–Zygmund operator
  topic: keywords
creator: Fan Bu
creator: Dachun Yang
creator: Wen Yuan
creator: Yuze Zhao
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-10
publication date: 2026-01-10
starting page: 371
ending page: 468
doi: 10.4208/ata.2025.deng90.08

δ-Universal Taylor Series
type: item
description: We present a new type of universal series, termed $\delta$-universal series, for which the sum of squared coefficients satisfies $$\sum\limits_{k=0}^{\infty} |a_k|^2 < \delta$$ for an arbitrarily small $\delta > 0$. We establish a version of Seleznev's theorem within this framework. To construct such $\delta$-universal series, we develop a variation of Mergelyan's theorem.
subject: Articles
  topic: section
subject: Universal series
  topic: keywords
subject: Seleznev’s Theorem
  topic: keywords
subject: Mergelyan’s theorem
  topic: keywords
subject: hardy space
  topic: keywords
creator: Wei Qu
creator: Shilin Wang
creator: Tao Qian
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-10
publication date: 2026-01-10
starting page: 1
ending page: 14
doi: 10.4208/ata.2025.deng90.07

A Signal Separation Method Based on Instantaneous Frequency Embedded Continuous Wavelet Transform and Short-Time Fourier Transform
type: item
description: Modeling a non-stationary, multicomponent signal as a superposition of frequency components, each with a well-defined instantaneous frequency (IF), is crucial for extracting information, such as the underlying dynamics hidden within the signal. The synchrosqueezing transform (SST) has emerged as an alternative to empirical mode decomposition (EMD) for separating non-stationary signals. However, because the SST estimates the IFs of all frequency components based on a single phase transformation, its accuracy can be limited. To address this, SST variants based on the IF-embedded short-time Fourier transform (IFE-STFT) and the IF-embedded continuous wavelet transform (IFE-CWT) were developed. More recently, a direct time-frequency method called the signal separation operation (SSO) was introduced for multicomponent signal separation. SSO bypasses the second step of the two-step SST method for component recovery and is based on variants of the STFT or CWT. In this paper, we propose a direct signal separation method by combining the SSO method with IFE-CWT and IFE-STFT, creating the IFE-CWT-based SSO (IWSSO) and the IFE-STFT-based SSO (IFSSO). Both IWSSO and IFSSO directly separate multicomponent signals without the squeezing operation inherent in SST. Our algorithms and techniques yield more accurate instantaneous frequency estimates and signal separation than conventional SSO or SST methods.
subject: Articles
  topic: section
subject: Instantaneous frequency (IF) estimation
  topic: keywords
subject: mode retrieval
  topic: keywords
subject: signal separation operator based on IF–embedded continuous wavelet transform
  topic: keywords
creator: Qingtang Jiang
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-10
publication date: 2026-01-10
starting page: 15
ending page: 31
doi: 10.4208/ata.2025.deng90.05

Singular Integral and Local Hardy Spaces in Dunkl Setting
type: item
description: The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in $L^2$ space and the theory of nonhomogeneous singular integral operators as pivotal components.
subject: Articles
  topic: section
subject: Nonhomogeneous Dunkl-Calderón-Zygmund singular integral
  topic: keywords
subject: local Dunkl-Hardy space
  topic: keywords
subject: weak local wavelet decomposition
  topic: keywords
creator: Yanchang Han
creator: Yongsheng Han
creator: Ji Li
creator: Chaoqiang Tan
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2026-01-10
publication date: 2026-01-10
starting page: 299
ending page: 370
doi: 10.4208/ata.2025.deng90.01

Weighted Boundedness of Toeplitz Type Operator Associated to General Singular Integral Operator Satisfying a Variant of Hörmander’s Condition
type: item
description: In this paper, we establish the weighted sharp maximal function inequalities for the Toeplitz type operator associated to the general singular integral operator satisfying a variant of Hörmander's condition. As an application, we obtain the boundedness of the operator on weighted Lebesgue and Morrey spaces.
subject: Articles
  topic: section
subject: Toeplitz type operator
  topic: keywords
subject: singular integral operator
  topic: keywords
subject: sharp maximal function
  topic: keywords
subject: weighted BMO
  topic: keywords
subject: weighted Lipschitz function.
  topic: keywords
subject: 42B20
  topic: subjects
subject: 42B25
  topic: subjects
creator: Lanzhe Liu
creator: Xiaoqi Zhou
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 284
ending page: 298
doi: 10.4208/ata.OA-2024-0020

Variable Exponent Central Morrey Estimates for Multilinear Bochner-Riesz Operators
type: item
description: We prove the boundedness of multilinear Bochner-Riesz operator on central Morrey spaces with variable exponents. Moreover, we also show that the variable exponent Lipschitz commutator of Bochner-Riesz operator are bounded on above spaces. As applications, we also obtain the bounds of the commutators generated by $\lambda$-central BMO functions and Bochner-Riesz operators on central Morrey spaces with variable exponents.
subject: Articles
  topic: section
subject: Multilinear Bochner-Riesz operator
  topic: keywords
subject: commutator
  topic: keywords
subject: central Morrey space with variable exponent
  topic: keywords
subject: boundedness.
  topic: keywords
subject: 42B15
  topic: subjects
subject: 42B20
  topic: subjects
subject: 42B35
  topic: subjects
creator: Yanqi Yang
creator: Lulu Yang
creator: Shuangping Tao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 259
ending page: 283
doi: 10.4208/ata.OA-2024-0022

Liouville Type Theorems for a Class of General Parabolic Hessian Quotient Type Equations
type: item
description: We first consider the a priori estimates to a class of general parabolic $(k,l)-$ Hessian quotient type equations of the form with $0{\le}1 or has interior gradient estimates and Pogorelov type estimates. As an application, we prove Liouville type theorems for these equations.
subject: Articles
  topic: section
subject: Parabolic $(k, l)$-Hessian quotient type equations
  topic: keywords
subject: Pogorelov type estimates
  topic: keywords
subject: Liouville type theorems
  topic: keywords
subject: 35K55
  topic: subjects
subject: 35B45
  topic: subjects
subject: 35B08
  topic: subjects
creator: Hui Liu
creator: Ni Xiang
creator: Lina Zheng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 238
ending page: 258
doi: 10.4208/ata.OA-2025-0006

A Rigidity Result for the Schiffer Conjecture on Domain with a Hole
type: item
description: Let $\Omega$ be a domain with a hole containing the origin in $\mathbb{R}^2$ and $u$ be a solution to the problem where $\partial^{\pm}\Omega$ represents the outer and inner boundaries of $\Omega,$ respectively, $c$ is a constant. Let ${\mu}_k$ denote the $k{\rm th}$ Neumann eigenvalue of the Laplacian on $\Omega$ and${\Omega}_h$ is the hole. We establish that if $\mu< {\mu}_8,$ then $\Omega$ is an annulus.
subject: Articles
  topic: section
subject: Schiffer conjecture
  topic: keywords
subject: overdetermined problem
  topic: keywords
subject: symmetry.
  topic: keywords
subject: 35J25
  topic: subjects
subject: 35N05
  topic: subjects
creator: Yingxin Sun
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 229
ending page: 237
doi: 10.4208/ata.OA-2024-0023

Estimates for Parabolic Schrödinger Operators with Certain Nonnegative Potentials
type: item
description: In this paper, the parabolic Schrödinger operator $\mathcal{P}={\partial}_t-\triangle+V(x)$ on $\mathbb{R}^{n+1}$ is considered, where $n\ge3,$ nonnegative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q \ge n /2$. The $L^p$ boundedness of operators $V^{\alpha}\mathcal{P}^{-\beta},$ $V^{\alpha}{\nabla}\mathcal{P}^{-\beta}$ and their adjoint operators are established.
subject: Articles
  topic: section
subject: $L^p$ estimate
  topic: keywords
subject: parabolic Schrödinger operator
  topic: keywords
subject: reverse Hölder class.
  topic: keywords
subject: 42B25
  topic: subjects
subject: 35J10
  topic: subjects
subject: 42B37
  topic: subjects
creator: Yanhui Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 197
ending page: 207
doi: 10.4208/ata.OA-2023-0009

Separation of Sequences and Multipliers in the Space of Tempered Distributions
type: item
description: We consider the notions of $v$-separation and $(N,v)$-separation for increasing sequences that tend to infinity. We study several of the connections between the properties of a multiplier in the space $S'(\mathbb{R})$ and in other related spaces and the separation properties of the sequence of its zeros. We also prove that a distributional division problem $$Fh=f,$$always has tempered solutions $h$ for any tempered data $f$ if and only if the non integrable function $1/F$ admits regularizations that are tempered, and that this holds if and only if the pseudofunction $\mathcal{P} f (1/F)$ is tempered.
subject: Articles
  topic: section
subject: Tempered distributions
  topic: keywords
subject: division problems
  topic: keywords
subject: separation of sequences.
  topic: keywords
subject: 46F10
  topic: subjects
creator: Ricardo Estrada
creator: Kevin Kellinsky-Gonzalez
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-29
publication date: 2025-09-29
starting page: 208
ending page: 228
doi: 10.4208/ata.OA-2024-0015

Double Cosine and Cosine-Sine Fourier Transforms and Generalized Lipschitz Classes in Uniform Metric
type: item
description: For complex-valued functions $f \in L^1(\mathbb{R}^2_+)$, where $\mathbb{R}_+ := [0,\infty)$ we give sufficient conditions under which the double cosine or cosine-sine Fourier transform of $f$ belongs to a generalized Lipschitz class defined by the mixed modulus of smoothness of orders $m,n \in \mathbb{N} = \{1,2,\cdots \}$ in uniform metric. The sharpness of these conditions is established under some restriction for non-negative functions.
subject: Articles
  topic: section
subject: double cosine and cosine-sine Fourier transform
  topic: keywords
subject: generalizrd Lipschits classes
  topic: keywords
subject: Boastype results
  topic: keywords
creator: Sergey Volosivets
creator: Yulia Krotova
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2025-09-15
publication date: 2025-09-15
doi: 10.4208/ata.OA-2022-0018

On Noveley Inequalities for Convex Stochastic Processes on Time Scale Utilizing Quantum Operators
type: item
description: We aim to present a innovation extension of the mean-square stochastic integral of a process on time scale based on a q-operator and fractional q-operator. By presenting the q-convex definition for a stochastic process and using quantum operators, we were able to prove some well-known inequalities such as the HermitHadamardand the Jensen for the processes.
subject: Articles
  topic: section
subject: Time scale
  topic: keywords
subject: fractional $q$-operator
  topic: keywords
subject: convex type stochastic processes
  topic: keywords
subject: inequalities
  topic: keywords
creator: Azizollah Babakhani
creator: Rosineide F. da Paz
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2025-09-15
publication date: 2025-09-15
doi: 10.4208/ata.OA-2024-0048

Multiplicity of Solutions for an Integro-Differential Equation with Trudinger-Moser Subcritical or Critical Nonlinearities
type: item
description: This paper study a general nonlocal problem characterized by the equation: \[ -\mathcal{L}_K u + V(x)u = P(x)h(u) \] in $\mathbb{R}$. Here, $\mathcal{L}_K$ represents a nonlocal integro-differential operator, and $h$ is a nonlinear term displaying subcritical or critical growth of Trudinger-Moser type. We initially prove the existence of a ground state solution by employing variational methods and innovative analytical approaches. Furthermore, through the application of constrained variational methods, Brouwer degree theory, and a quantitative deformation lemma, we establish the existence of a sign-changing solution with minimal energy, surpassing the energy of the ground state solution.
subject: Articles
  topic: section
subject: Nonlocal problem
  topic: keywords
subject: fractional Laplacian
  topic: keywords
subject: sign-changing solutions
  topic: keywords
creator: Ying Cai
creator: Guangze Gu
creator: Zhipeng Yang
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2025-09-15
publication date: 2025-09-15
doi: 10.4208/ata.OA-2025-0002