Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality

Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞....

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Bibliographic Details
Published in:Analysis in theory & applications 2014, Vol.30 (2), p.193-204
Main Author: Zuoshunhua Shi Wu Di Dunyan Yan
Format: Article
Language:English
Subjects:
Hardy
Lorentz空间
Sobolev不等式
充分必要条件
充要条件
加权
卷积定理
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Summary:Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞.
ISSN:1672-4070
1573-8175
DOI:10.4208/ata.2014.v30.n2.5