{"paper":{"title":"On the growth of the optimal constants of the multilinear Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Nu\\~nez-Alarc\\'on, Daniel Pellegrino","submitted_at":"2012-05-10T20:31:32Z","abstract_excerpt":"Let $(K_{n})_{n=1}^{\\infty}$ be the optimal constants satisfying the multilinear (real or complex) Bohnenblust--Hille inequality. The exact values of the constants $K_{n}$ are still waiting to be discovered since eighty years ago; recently, it was proved that $(K_{n})_{n=1}^{\\infty}$ has a subexponential growth. In this note we go a step further and address the following question: Is it true that \\[ \\lim_{n\\rightarrow\\infty}(K_{n}-K_{n-1}) =0? \\] Our main result is a Dichotomy Theorem for the constants satisfying the Bohnenblust--Hille inequality; in particular we show that the answer to the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2385","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"}