{"paper":{"title":"Optimal constants for a mixed Littlewood type inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel N\\'u\\~nez-Alarc\\'on, Daniel Pellegrino, Tony Nogueira","submitted_at":"2016-04-21T14:30:51Z","abstract_excerpt":"For $p\\in\\lbrack2,\\infty]$ a mixed Littlewood-type inequality asserts that there is a constant $C_{(m),p}\\geq1$ such that \\[ \\left( \\sum_{i_{1}=1}^{\\infty}\\left( \\sum_{i_{2},...,i_{m}=1}^{\\infty }|T(e_{i_{1}},...,e_{i_{m}})|^{2}\\right) ^{\\frac{1}{2}\\frac{p}{p-1}}\\right) ^{\\frac{p-1}{p}}\\leq C_{(m),p}\\Vert T\\Vert \\] for all continuous real-valued $m$-linear forms on $\\ell_{p}\\times c_{0} \\times\\dots\\times c_{0}$ (when $p=\\infty$, $\\ell_{p}$ is replaced by $c_{0})$. We prove that for $p>2.18006$ the optimal constants $C_{(m),p}$ are $\\left( 2^{\\frac{1}{2}-\\frac{1}{p}}\\right) ^{m-1}.$ When $p=\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06323","kind":"arxiv","version":2},"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"}