Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality (Analysis in Theory and Applications, 2014)
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., $0< p\le ∞$ and $0< q\le ∞$.