{"paper":{"title":"The optimal constants for the real Hardy--Littlewood inequality for bilinear forms on $c_{0}\\times\\ell_{p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Daniel Nunez-Alarcon, Daniel Pellegrino","submitted_at":"2015-08-10T19:05:00Z","abstract_excerpt":"For $p,q\\geq2$, the Hardy and Littlewood inequalities for real bilinear forms, in its unified formulation, assert that there is a constant $C_{p,q}\\geq1$ such that \\begin{equation} \\left(\\sum\\limits_{j=1}^{\\infty}\\left(\\sum\\limits_{k=1}^{\\infty}\\left\\vert A(e_{j},e_{k})\\right\\vert ^{2}\\right) ^{\\frac{\\lambda}{2}}\\right) ^{\\frac {1}{\\lambda}}\\leq C_{p,q}\\left\\Vert A\\right\\Vert, \\end{equation} with sharp exponent $\\lambda=\\frac{pq}{pq-p-q},$ for all continuous bilinear forms $A:\\ell_{p}\\times\\ell_{q}\\rightarrow\\mathbb{R}$ (as usual, $c_{0}$ replaces $\\ell_{p}$ or $\\ell_{q}$ when $p=\\infty$ or $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02355","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"}