TY - JOUR
T1 - Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality
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 - <p style="text-align: justify;">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., $0&lt; p\le \infty$ and $0&lt; q\le \infty$.</p>