{"paper":{"title":"Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Pellegrino, G. A. Mu\\~noz-Fern\\'andez, J. B. Seoane-Sep\\'ulveda","submitted_at":"2011-07-24T23:52:30Z","abstract_excerpt":"A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$(\\sum\\limits_{i_{1},...,i_{n}=1}^{N}|U(e_{i_{^{1}}},...,e_{i_{n}})|^{\\frac{2n}{n+1}})^{\\frac{n+1}{2n}}\\leq C_{n}||U||$$ for every positive integer $N$ and every $n$-linear mapping $U:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow\\mathbb{C}$. The original estimates for those constants from Bohnenblust and Hille are $$C_{n}=n^{\\frac{n+1}{2n}}2^{\\frac{n-1}{2}}.$$ In this note we present explicit formulae for quite better constants, and calcul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4814","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"}