{"paper":{"title":"Reversed Hardy-Littewood-Sobolev inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingbo Dou, Meijun Zhu","submitted_at":"2013-09-08T16:33:58Z","abstract_excerpt":"The classical sharp Hardy-Littlewood-Sobolev inequality states that, for $1<p, t<\\infty$ and $0<\\lambda=n-\\alpha <n$ with $ 1/p +1 /t+ \\lambda /n=2$, there is a best constant $N(n,\\lambda,p)>0$, such that $$ |\\int_{\\mathbb{R}^n} \\int_{\\mathbb{R}^n} f(x)|x-y|^{-\\lambda} g(y) dx dy|\\le N(n,\\lambda,p)||f||_{L^p(\\mathbb{R}^n)}||g||_{L^t(\\mathbb{R}^n)} $$ holds for all $f\\in L^p(\\mathbb{R}^n), g\\in L^t(\\mathbb{R}^n).$ The sharp form is due to Lieb, who proved the existence of the extremal functions to the inequality with sharp constant, and computed the best constant in the case of $p=t$ (or one of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1974","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}