{"paper":{"title":"Multilinear Marcinkiewicz-Zygmund inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Daniel Carando, Martin Mazzitelli, Sheldy Ombrosi","submitted_at":"2016-11-24T18:56:30Z","abstract_excerpt":"We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on $\\ell^r$-valued extensions of linear operators. We show that for certain $1 \\leq p, q_1, \\dots, q_m, r \\leq \\infty$, there is a constant $C\\geq 0$ such that for every bounded multilinear operator $T\\colon L^{q_1}(\\mu_1) \\times \\cdots \\times L^{q_m}(\\mu_m) \\to L^p(\\nu)$ and functions $\\{f_{k_1}^1\\}_{k_1=1}^{n_1} \\subset L^{q_1}(\\mu_1), \\dots, \\{f_{k_m}^m\\}_{k_m=1}^{n_m} \\subset L^{q_m}(\\mu_m)$, the following inequality holds \\begin{equation}\\label{MZ ineq abstract} (1) \\quad \\quad \\left\\Vert \\left(\\sum_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08284","kind":"arxiv","version":3},"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"}