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Volume 39, Issue 2
The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces

Dan Xiao & Lisheng Shu

Anal. Theory Appl., 39 (2023), pp. 163-177.

Published online: 2023-06

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  • Abstract

Under some natural regularity assumptions on the exponent function, we obtain the boundedness of Marcinkiewicz integrals $\mu,$ $\mu^ρ_S$ and $\mu^{∗,ρ}_λ$ on grand variable Herz spaces. Our results enrich and improve some previous results in the literature.

  • AMS Subject Headings

46E30, 42B35

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COPYRIGHT: © Global Science Press

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@Article{ATA-39-163, author = {Xiao , Dan and Shu , Lisheng}, title = {The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {2}, pages = {163--177}, abstract = {

Under some natural regularity assumptions on the exponent function, we obtain the boundedness of Marcinkiewicz integrals $\mu,$ $\mu^ρ_S$ and $\mu^{∗,ρ}_λ$ on grand variable Herz spaces. Our results enrich and improve some previous results in the literature.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0007}, url = {http://global-sci.org/intro/article_detail/ata/21821.html} }
TY - JOUR T1 - The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces AU - Xiao , Dan AU - Shu , Lisheng JO - Analysis in Theory and Applications VL - 2 SP - 163 EP - 177 PY - 2023 DA - 2023/06 SN - 39 DO - http://doi.org/10.4208/ata.OA-2021-0007 UR - https://global-sci.org/intro/article_detail/ata/21821.html KW - Marcinkiewicz integrals, Herz spaces, variable exponent, grand spaces. AB -

Under some natural regularity assumptions on the exponent function, we obtain the boundedness of Marcinkiewicz integrals $\mu,$ $\mu^ρ_S$ and $\mu^{∗,ρ}_λ$ on grand variable Herz spaces. Our results enrich and improve some previous results in the literature.

Xiao , Dan and Shu , Lisheng. (2023). The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces. Analysis in Theory and Applications. 39 (2). 163-177. doi:10.4208/ata.OA-2021-0007
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