{"paper":{"title":"Improved bounds in the metric cotype inequality for Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Assaf Naor, Manor Mendel, Ohad Giladi","submitted_at":"2010-03-01T08:50:42Z","abstract_excerpt":"It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m< n^{1+1/q}$ such that for every f:Z_m^n --> X we have\n$\\sum_{j=1}^n \\Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] < C m^q \\Avg_{\\e,x} [ ||f(x+\\e)-f(x) ||_X^q ]$,\nwhere the expectations are with respect to uniformly chosen x\\in Z_m^n and \\e\\in \\{-1,0,1\\}^n, and all the implied constants may depend only on q and the Rademacher cotype q constant of X. This improves the bound of m< n^{2+\\frac{1}{q}} from [Mendel, Naor 2008]. The proof of the above inequality is based on a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0279","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"}