{"paper":{"title":"The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Diogo Diniz, G. A. Mu\\~noz-Fern\\'andez, J. B. Seoane-Sep\\'ulveda","submitted_at":"2011-08-07T15:31:24Z","abstract_excerpt":"We provide (for both the real and complex settings) a family of constants, $% (C_{m})_{m\\in \\mathbb{N}}$, enjoying the Bohnenblust--Hille inequality and such that $\\displaystyle\\lim_{m\\rightarrow \\infty}\\frac{C_{m}}{C_{m-1}}=1$, i.e., their asymptotic growth is the best possible. As a consequence, we also show that the optimal constants, $(K_{m})_{m\\in \\mathbb{N}}$, in the Bohnenblust--Hille inequality have the best possible asymptotic behavior. Besides its intrinsic mathematical interest and potential applications to different areas, the importance of this result also lies in the fact that al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1550","kind":"arxiv","version":2},"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"}