{"paper":{"title":"Universal bounds for the Hardy--Littlewood inequalities on multilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gustavo Ara\\'ujo, Kleber C\\^amara","submitted_at":"2018-03-04T18:23:07Z","abstract_excerpt":"The Hardy--Littlewood inequalities for multilinear forms on sequence spaces state that for all positive integers $m,n\\geq2$ and all $m$-linear forms $T:\\ell_{p_{1}}^{n}\\times\\cdots\\times\\ell_{p_{m}}^{n}\\rightarrow\\mathbb{K}$ ($\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$) there are constants $C_{m}\\geq1$ (not depending on $n$) such that \\[ \\left( \\sum_{j_{1},\\ldots,j_{m}=1}^{n}\\left\\vert T(e_{j_{1}},\\ldots,e_{j_{m}})\\right\\vert ^{\\rho}\\right) ^{\\frac{1}{\\rho}}\\leq C_{m}\\sup_{\\left\\Vert x_{1}\\right\\Vert ,\\dots,\\left\\Vert x_{m}\\right\\Vert \\leq 1}\\left\\vert T(x_{1},\\dots,x_{m})\\right\\vert, \\] where $\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01397","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"}