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Volume 34, Issue 4
Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces

Dan Xiao & Lisheng Shu

Commun. Math. Res., 34 (2018), pp. 371-382.

Published online: 2019-12

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  • Abstract

In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extends some known results.

  • Keywords

Marcinkiewicz integral, variable exponent, Muckenhoupt weight, Herz-Morrey space

  • AMS Subject Headings

46E30, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

smilexd163@163.com (Dan Xiao)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-371, author = {Dan and Xiao and smilexd163@163.com and 5993 and Department of Basic Courses, Anhui Professional College of Art, Hefei, 230001 and Dan Xiao and Lisheng and Shu and and 5521 and School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui, 241003 and Lisheng Shu}, title = {Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {4}, pages = {371--382}, abstract = {

In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extends some known results.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.04.10}, url = {http://global-sci.org/intro/article_detail/cmr/13513.html} }
TY - JOUR T1 - Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces AU - Xiao , Dan AU - Shu , Lisheng JO - Communications in Mathematical Research VL - 4 SP - 371 EP - 382 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.04.10 UR - https://global-sci.org/intro/article_detail/cmr/13513.html KW - Marcinkiewicz integral, variable exponent, Muckenhoupt weight, Herz-Morrey space AB -

In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extends some known results.

Dan Xiao & Lisheng Shu. (2019). Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces. Communications in Mathematical Research . 34 (4). 371-382. doi:10.13447/j.1674-5647.2018.04.10
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