{"paper":{"title":"When are the Hardy-Littlewood inequalities contractive?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D.M. Pellegrino, J. Santos, P. Rueda, T. Nogueira, W.V. Cavalcante","submitted_at":"2017-05-17T18:39:38Z","abstract_excerpt":"The optimal constants of the $m$-linear Bohnenblust-Hille and Hardy-Littlewood inequalities are still not known despite its importance in several fields of Mathematics. For the Bohnenblust-Hille inequality and real scalars it is well-known that the optimal constants are not contractive. In this note, among other results, we show that if we consider sums over $M:=M(m)$ indexes with $M\\log M=o(m)$, the optimal constants are contractive. For instance, we can consider% \\[ M=\\left\\lfloor \\frac{m}{\\left( \\log m\\right) ^{1+\\frac{1}{\\log\\log\\log m}}% }\\right\\rfloor \\] where $\\lfloor x\\rfloor:=\\max\\{n\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06307","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"}