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Volume 39, Issue 1
Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator

Qianjun He, Mingquan Wei & Dunyan Yan

DOI: 10.4208/ata.OA-2020-0039

Anal. Theory Appl., 39 (2023), pp. 28-41.

Published online: 2023-03

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  • Abstract

In this paper, we calculate the sharp bound for the generalized $m$-linear $n$-dimensional Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces, which generalizes the previous results.

  • Keywords

Sharp bound, $n$-dimensional Hardy-Littlewood-Pόlya operator, power weight, Morrey space, Hausdorff operator.

  • AMS Subject Headings

42B25, 26D15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-39-28, author = {He , QianjunWei , Mingquan and Yan , Dunyan}, title = {Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {1}, pages = {28--41}, abstract = {

In this paper, we calculate the sharp bound for the generalized $m$-linear $n$-dimensional Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces, which generalizes the previous results.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0039}, url = {http://global-sci.org/intro/article_detail/ata/21459.html} }
TY - JOUR T1 - Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator AU - He , Qianjun AU - Wei , Mingquan AU - Yan , Dunyan JO - Analysis in Theory and Applications VL - 1 SP - 28 EP - 41 PY - 2023 DA - 2023/03 SN - 39 DO - http://doi.org/10.4208/ata.OA-2020-0039 UR - https://global-sci.org/intro/article_detail/ata/21459.html KW - Sharp bound, $n$-dimensional Hardy-Littlewood-Pόlya operator, power weight, Morrey space, Hausdorff operator. AB -

In this paper, we calculate the sharp bound for the generalized $m$-linear $n$-dimensional Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces, which generalizes the previous results.

Qianjun He, Mingquan Wei & Dunyan Yan. (2023). Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator. Analysis in Theory and Applications. 39 (1). 28-41. doi:10.4208/ata.OA-2020-0039
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