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

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

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

Published online: 2014-06

Preview Full PDF 283 1117
Export citation
  • Abstract

Using product and convolution theorems on Lorentz spaces, wecharacterize the sufficient and necessary conditions which ensure thevalidity of the doubly weighted Hardy-Littlewood-Sobolevinequality. It should be pointed out that we consider whole rangesof $p$ and $q$, i.e., $0< p\le \infty$ and $0< q\le \infty$.

  • Keywords

H\"{o}lder's inequality Young's inequality Hardy-Littlewood-Sobolev inequality Lorentz space

  • AMS Subject Headings

42B20 42B35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
Copy to clipboard
The citation has been copied to your clipboard