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Volume 54, Issue 3
On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents

Chenglong Fang & Jiang Zhou

DOI: 10.4208/jms.v54n3.21.01

J. Math. Study, 54 (2021), pp. 227-249.

Published online: 2021-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

42B35, 42C40, 46E30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fangclmath@126.com (Chenglong Fang)

zhoujiang@xju.edu.cn (Jiang Zhou)

  • BibTex
  • RIS
  • TXT
@Article{JMS-54-227, author = {Fang , Chenglong and Zhou , Jiang}, title = {On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {3}, pages = {227--249}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n3.21.01}, url = {http://global-sci.org/intro/article_detail/jms/18733.html} }
TY - JOUR T1 - On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents AU - Fang , Chenglong AU - Zhou , Jiang JO - Journal of Mathematical Study VL - 3 SP - 227 EP - 249 PY - 2021 DA - 2021/03 SN - 54 DO - http://doi.org/10.4208/jms.v54n3.21.01 UR - https://global-sci.org/intro/article_detail/jms/18733.html KW - 2-microlocal, variable exponent, Herz type spaces, Besov spaces, Triebel-Lizorkin spaces, Peetre's maximal operator. AB -

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.

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