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: 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: Liouville Type Theorems for a Class of General Parabolic Hessian Quotient Type Equations
items: Variable Exponent Central Morrey Estimates for Multilinear Bochner-Riesz Operators
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
items: Two-Weight Inequality of Calderón-Zygmund Operator on Non-Homogeneous Metric Measure Space
items: On Non-Linearly Coupled Schrodinger Systems
items: Decomposition Formulas of Kampé de Fériets Double Hypergeometric Functions
items: Erdös Type Inequality for Lorentz Polynomials
items: Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders
items: Some Characterizations of Bloch Functions
items: Weighted Boundedness of Commutators of Generalized Calderόn-Zygmund Operators
items: Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p
items: Hopf Bifurcation of a Nonresident Computer Virus Model with Delay

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

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

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

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

Two-Weight Inequality of Calderón-Zygmund Operator on Non-Homogeneous Metric Measure Space
type: item
description: Let $(\mathcal{X}, d, \mu)$ be a non-homogeneous metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, we study weighted inequalities of the Calder\'{o}n-Zygmund operator on $(\mathcal{X}, d, \mu)$. Specifically, for $1 < p < \infty$, we identify sufficient conditions for the weight on one side, which guarantee the existence of another weight in the other side, so that the weighted $L^p$ inequality holds. We deal with this problem by developing a vector-valued theory for Calder\'{o}n-Zygmund operators on the non-homogeneous metric measure spaces which is interesting in its own right.
subject: Articles
  topic: section
subject: Non-homogeneous metric measure space
  topic: keywords
subject: Calderón-Zygmund operator
  topic: keywords
subject: vector-valued inequality
  topic: keywords
subject: weighted inequality
  topic: keywords
creator: Yaoyao Han
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2025-09-15
publication date: 2025-09-15
doi: 10.4208/ata.OA-2024-0019

On Non-Linearly Coupled Schrodinger Systems
type: item
description: Abstract. In this paper we study the following nonlinear Schr\"{o}dinger system: \[ \begin{cases} -\Delta u + a(x) u = \lambda(x) f(u, v), & x \in \mathbb{R}^N, \\ -\Delta v + b(x) v = \lambda(x) g(u, v), & x \in \mathbb{R}^N, \\ u(x) \to 0, & v(x) \to 0 \end{cases} \] as $ |x| \to \infty $. Here, $ a, b, \lambda \in C(\mathbb{R}^N, \mathbb{R}) $ are all non-periodic in $ x_i $ for $ i = 1, \cdots, N, N \geq 3, f, g \in C(\mathbb{R}^2, \mathbb{R}) $. We show that this system has infinitely many solutions with small negative energies and infinitely many large-energy solutions. To the best of our knowledge, there is no corresponding result about such a Schr\"{o}dinger system.
subject: Articles
  topic: section
subject: to be provided by authors
  topic: keywords
creator: Jing Zhang
rights: Copyright (c) 2025 Analysis in Theory and Applications
date: 2025-09-15
publication date: 2025-09-15
doi: 10.4208/ata.OA-2025-0014

Decomposition Formulas of Kampé de Fériets Double Hypergeometric Functions
type: item
description: This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kamp\u00e9 de F\u00e9riets series of double hypergeometric series $F^{p:q;k}_{l:m;n}$.
subject: Articles
  topic: section
subject: Generalized hypergeometric function
  topic: keywords
subject: Kampé de Fériets functions
  topic: keywords
subject: decomposition formulas
  topic: keywords
subject: inverse pairs of symbolic operators.
  topic: keywords
subject: 35K65
  topic: subjects
subject: 33C20
  topic: subjects
subject: 33C65
  topic: subjects
creator: Maged G. Bin-Saad, Anvar Hasanov & Mamasali Turaev
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 275
ending page: 292
doi: 10.4208/ata.OA-2017-0077

Erdös Type Inequality for Lorentz Polynomials
type: item
description: An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In the present paper, we give two classes of Lorentz polynomials, for which the Erd\u00f6s-type inequality holds.
subject: Articles
  topic: section
subject: Lorentz representation of polynomials
  topic: keywords
subject: constrained polynomials
  topic: keywords
subject: Morkov-type inequalities
  topic: keywords
subject: Erdös-type inequality.
  topic: keywords
subject: 11C08
  topic: subjects
subject: 41A17
  topic: subjects
creator: Laiyi Zhu, Dapeng Zhou & Zhiyong Huang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 232
ending page: 240
doi: 10.4208/ata.OA-2017-0002

Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders
type: item
description: In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach\u2019s fixed point theorem, Leray-Schauder\u2019s nonlinear alternative and Leray-Schauder\u2019s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.
subject: Articles
  topic: section
subject: Riemann-Liouville integral
  topic: keywords
subject: existence
  topic: keywords
subject: fixed point theorem
  topic: keywords
subject: Leray-Schauder alternative.
  topic: keywords
subject: 26A33
  topic: subjects
subject: 34A12
  topic: subjects
subject: 34A08
  topic: subjects
creator: Mohamed Houas
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 253
ending page: 274
doi: 10.4208/ata.OA-2017-0021

Some Characterizations of Bloch Functions
type: item
description: We define Bloch-type functions of $\mathcal{C}^1(\mathbb{D})$ on the unit disk of complex plane $\mathbb{C}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_{\phi}$\u00a0acting between two Bloch-type spaces. These obtained results generalize the corresponding known ones to the setting of $\mathcal{C}^1(\mathbb{D})$.
subject: Articles
  topic: section
subject: Bloch space
  topic: keywords
subject: majorant
  topic: keywords
subject: composition operator.
  topic: keywords
subject: 11K70
  topic: subjects
subject: 32A70
  topic: subjects
creator: Guanghua He
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 225
ending page: 231
doi: 10.4208/ata.OA-2017-0059

Weighted Boundedness of Commutators of Generalized Calderόn-Zygmund Operators
type: item
description: $[b,T]$ denotes the commutator of generalized Calder\u00f3n-Zygmund operators $T$ with Lipschitz function $b$, where $b \u2208 \rm{Lip}_\u03b2(R^n)$, $(0<\u03b2\u22641)$ and $T$ is a $\u03b8(t)$\u2212type Calder\u00f3n-Zygmund operator. The commutator $[b,T]$ generated by $b$ and $T$ is defined by\u00a0 $$[b,T] f(x)=b(x)Tf(x)\u2212T(bf)(x)=\u222bk(x,y)(b(x)\u2212b(y))f(y)dy.$$ In this paper, the authors discuss the boundedness of the commutator $[b,T]$ on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that $[b,T]$ is bounded from $H^p(\u03c9^p)$ to $L^q(\u03c9^q)$, and from $H\dot{K}^{\u03b1,p}_{q_1}(\u03c9_1,\u03c9^{q_1}_2)$ to $\dot{K}^{\u03b1,p}_{q_2}(\u03c9_1,\u03c9^{q_2}_2)$. The results extend and generalize the well-known ones in [7].
subject: Articles
  topic: section
subject: Commutator
  topic: keywords
subject: Lipschitz function
  topic: keywords
subject: weighted hardy space
  topic: keywords
subject: Herz space.
  topic: keywords
subject: 42B20
  topic: subjects
subject: 42B25
  topic: subjects
creator: Cuilan Wu, Yunjie Wang & Lisheng Shu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 209
ending page: 224
doi: 10.4208/ata.OA-2017-0050

Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p
type: item
description: In this study, as the domain of four dimensional Euler mean $E(r,s)$ of orders $r$, $s$ in the space $\mathcal{L}_p$ for $0<p<1$, we examine the double sequence space $\varepsilon^{r,s}_p$ and some properties of four dimensional Euler mean. We determine the $\u03b1$- and $\u03b2(bp)$-duals of the space $\varepsilon^{r,s}_p$, and characterize the classes $(\varepsilon^{r,s}_p:\mathcal{M}_u)$,\u00a0$(\varepsilon^{r,s}_p:\mathcal{C}_{bp})$\u00a0and $(\varepsilon^{r,s}_p:\mathcal{L}_q)$ of four dimensional matrix transformations, where $1\u2264q<\u221e$. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.
subject: Articles
  topic: section
subject: Summability theory
  topic: keywords
subject: double sequences
  topic: keywords
subject: double series
  topic: keywords
subject: alpha-
  topic: keywords
subject: beta- and gamma-duals
  topic: keywords
subject: matrix domain of 4-dimensional matrices
  topic: keywords
subject: matrix transformations.
  topic: keywords
subject: 46A45
  topic: subjects
subject: 40C05
  topic: subjects
creator: Medine Ye\u015filkayagil & Feyzi Ba\u015far
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 241
ending page: 252
doi: 10.4208/ata.OA-2017-0056

Hopf Bifurcation of a Nonresident Computer Virus Model with Delay
type: item
description: In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.
subject: Articles
  topic: section
subject: Computer virus
  topic: keywords
subject: delay
  topic: keywords
subject: Hopf bifurcation
  topic: keywords
subject: SLA model
  topic: keywords
subject: Periodic solution.
  topic: keywords
subject: 34C15
  topic: subjects
subject: 34C23
  topic: subjects
subject: 37G15
  topic: subjects
subject: 37N25
  topic: subjects
creator: Zizhen Zhang, Yougang Wang & Massimiliano Ferrara
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2018-11-14
publication date: 2018-11-14
starting page: 199
ending page: 208
doi: 10.4208/ata.OA-2016-0035