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Volume 30, Issue 2
Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality

Z. Shi, W. Di & D. Y. Yan

DOI: 10.4208/ata.2014.v30.n2.5

Anal. Theory Appl., 30 (2014), pp. 193-204.

Published online: 2014-06

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  • 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 $0< q\le \infty$.

  • Keywords

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

  • AMS Subject Headings

42B20, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-30-193, author = {Z. Shi, W. Di and D. Y. Yan}, title = {Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {2}, pages = {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 $0< q\le \infty$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n2.5}, url = {http://global-sci.org/intro/article_detail/ata/4484.html} }
TY - JOUR T1 - Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality AU - Z. Shi, W. Di & D. Y. Yan JO - Analysis in Theory and Applications VL - 2 SP - 193 EP - 204 PY - 2014 DA - 2014/06 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n2.5 UR - https://global-sci.org/intro/article_detail/ata/4484.html KW - Hölder's inequality, Young's inequality, Hardy-Littlewood-Sobolev inequality, Lorentz space. AB -

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 $0< q\le \infty$.

Z. Shi, W. Di and D. Y. Yan. (2014). Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality. Analysis in Theory and Applications. 30 (2). 193-204. doi:10.4208/ata.2014.v30.n2.5
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