{"paper":{"title":"Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Congming Li, Genggeng Huang, Ximing Yin","submitted_at":"2013-09-17T06:37:55Z","abstract_excerpt":"In this paper, we study the best constant of the following discrete Hardy-Littlewood-Sobolev inequality, \\begin{equation} \\sum_{i,j,i\\neq j}\\frac{f_{i}g_{j}}{\\mid i-j\\mid^{n-\\alpha}}\\leq C_{r,s,\\alpha} |f|_{l^r} |g|_{l^s}, \\end{equation}where $i,j\\in \\mathbb Z^n$, $r,s>1$, $0<\\alpha<n$, and $\\frac 1r+\\frac 1s+\\frac {n-\\alpha}n\\geq 2$. Indeed, we can prove that the best constant is attainable in the supercritical case $\\frac 1r+\\frac 1s+\\frac {n-\\alpha}n> 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4196","kind":"arxiv","version":1},"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"}