3.9 Article

Sharp Bound for the Generalized m-Linear n-Dimensional Hardy-Littlewood-Po?lya Operator

期刊

ANALYSIS IN THEORY AND APPLICATIONS
卷 39, 期 1, 页码 28-41

出版社

GLOBAL SCIENCE PRESS
DOI: 10.4208/ata.OA-2020-0039

关键词

Sharp bound; n-dimensional Hardy-Littlewood-P?lya operator; power weight; Mor-rey space; Hausdorff operator

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In this paper, we compute the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces. An application of this is obtaining the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces. Finally, the sharp bound for the Hausdorff operator on power weighted central and non-central homogeneous Morrey spaces is also found, generalizing previous results.
In this paper, we calculate the sharp bound for the generalized m-linear n -dimensional Hardy-Littlewood-Polya operator on power weighted central and non -central homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous 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.

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