{"paper":{"title":"The optimal constants of the mixed $\\left( \\ell_{1},\\ell _{2}\\right) $-Littlewood inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino","submitted_at":"2015-01-05T20:33:25Z","abstract_excerpt":"In this note, among other results, we find the optimal constants of the generalized Bohnenblust--Hille inequality for $m$-linear forms over $\\mathbb{R}$ and with multiple exponents $\\left( 1,2,...,2\\right) $, sometimes called mixed $\\left( \\ell _{1},\\ell _{2}\\right) $-Littlewood inequality. We show that these optimal constants are precisely $\\left( \\sqrt{2}\\right) ^{m-1}$ and this is somewhat surprising since a series of recent papers have shown that similar constants have a sublinear growth. This result answers a question raised by Albuquerque \\textit{et al.} in a paper published in 2014 in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00965","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"}