{"paper":{"title":"Summability of multilinear forms on classical sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pilar Rueda, Tony Nogueira","submitted_at":"2016-04-06T13:27:33Z","abstract_excerpt":"We present an extension of the Hardy--Littlewood inequality for multilinear forms. More precisely, let $\\mathbb{K}$ be the real or complex scalar field and $m,k$ be positive integers with $m\\geq k\\,$ and $n_{1},\\dots ,n_{k}$ be positive integers such that $n_{1}+\\cdots +n_{k}=m$.\n  ($a$) If $(r,p)\\in (0,\\infty )\\times \\lbrack 2m,\\infty ]$ then there is a constant $D_{m,r,p,k}^{\\mathbb{K}}\\geq 1$ (not depending on $n$) such that $$ \\left( \\sum_{i_{1},\\dots ,i_{k}=1}^{n}\\left| T\\left( e_{i_{1}}^{n_{1}},\\dots ,e_{i_{k}}^{n_{k}}\\right) \\right| ^{r}\\right) ^{% \\frac{1}{r}}\\leq D_{m,r,p,k}^{\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01610","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"}