@Article{ATA-30-193, author = {}, 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} }