On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents

Authors

  • Chenglong Fang School of Mathematics, Renmin University of China, Beijing 100872, China
  • Jiang Zhou College of Mathematical Sciences, Xinjiang University, Urumqi 830000, China

DOI:

https://doi.org/10.4208/jms.v54n3.21.01

Keywords:

2-microlocal, variable exponent, Herz type spaces, Besov spaces, Triebel-Lizorkin spaces, Peetre's maximal operator.

Abstract

In this paper, 2-microlocal Herz type Besov and Triebel-Lizorkin spaces with variable exponents are introduced for the first time. Then, we give characterizations of these spaces by so-called Peetre's maximal functions. Further, the atomic and molecular decompositions of these spaces are obtained. Finally, using the characterizations of the spaces by local means and molecular decomposition we obtain the wavelet characterizations.

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Published

2021-03-29

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Issue

Vol. 54 No. 3 (2021)

Section

Articles

How to Cite

On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents. (2021). Journal of Mathematical Study, 54(3), 227-249. https://doi.org/10.4208/jms.v54n3.21.01