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

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

Year:    2014

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 2 : pp. 193–204

Abstract

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 consider whole ranges of $p$ and $q$, i.e., $0< p\le \infty$ and $0< q\le \infty$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2014.v30.n2.5

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 2 : pp. 193–204

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Hölder's inequality Young's inequality Hardy-Littlewood-Sobolev inequality Lorentz space.

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