{"paper":{"title":"Optimal Hardy--Littlewood inequalities uniformly bounded by a universal constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Pellegrino, G. Ara\\'ujo, J. Santos, M. Maia, N. Albuquerque, T. Nogueira","submitted_at":"2016-09-10T18:59:47Z","abstract_excerpt":"The Hardy--Littlewood inequality for $m$-linear forms on $\\ell _{p}$ spaces and $m<p\\leq 2m$ asserts that \\begin{equation*} \\left( \\sum_{j_{1},...,j_{m}=1}^{\\infty }\\left\\vert T\\left( e_{j_{1}},\\ldots ,e_{j_{m}}\\right) \\right\\vert ^{\\frac{p}{p-m}}\\right) ^{\\frac{p-m}{p}}\\leq 2^{\\frac{m-1}{2}}\\left\\Vert T\\right\\Vert \\end{equation*} for all continuous $m$-linear forms $T:\\ell _{p}\\times \\cdots \\times \\ell _{p}\\rightarrow \\mathbb{R}$ or $\\mathbb{C}.$ The case $m=2$ recovers a classical inequality proved by Hardy and Littlewood in 1934. As a consequence of the results of the present paper we show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03081","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"}