{"paper":{"title":"Optimal exponents for Hardy--Littlewood inequalities for $m$-linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. M. Serrano-Rodr\\'iguez, D. N\\'u\\~nez-Alarc\\'on, D. Pellegrino, R. M. Aron","submitted_at":"2016-01-31T00:39:32Z","abstract_excerpt":"The Hardy--Littlewood inequalities on $\\ell _{p}$ spaces provide optimal exponents for some classes of inequalities for bilinear forms on $\\ell _{p}$ spaces. In this paper we investigate in detail the exponents involved in Hardy--Littlewood type inequalities and provide several optimal results that were not achieved by the previous approaches. Our first main result asserts that for $q_{1},...,q_{m}>0$ and an infinite-dimensional Banach space $Y$ attaining its cotype $\\cot Y$, if \\begin{equation*} \\frac{1}{p_{1}}+...+\\frac{1}{p_{m}}<\\frac{1}{\\cot Y}, \\end{equation*} then the following assertion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00178","kind":"arxiv","version":4},"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"}