{"paper":{"title":"There exist multilinear Bohnenblust-Hille constants $(C_{n})_{n=1}^{\\infty}$ with $\\displaystyle \\lim_{n\\rightarrow \\infty}(C_{n+1}-C_{n}) =0.$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Nunez-Alarcon, Daniel Pellegrino, Diana M. Serrano-Rodriguez, Juan Seoane-Sepulveda","submitted_at":"2012-06-30T18:46:20Z","abstract_excerpt":"The $n$-linear Bohnenblust-Hille inequality asserts that there is a constant $C_{n}\\in\\lbrack1,\\infty)$ such that the $\\ell_{\\frac{2n}{n+1}}$-norm of $(U(e_{i_{^{1}}},...,e_{i_{n}}))_{i_{1},...i_{n}=1}^{N}$is bounded above by $C_{n}$ times the supremum norm of $U,$ regardless of the $n$-linear form $U:\\mathbb{C}^{N}\\times...\\times\\mathbb{C}^{N}% \\rightarrow\\mathbb{C}$ and the positive integer $N$ (the same holds for real scalars). The power $2n/(n+1)$ is sharp but the values and asymptotic behavior of the optimal constants remain a mystery. The first estimates for these constants had exponenti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0124","kind":"arxiv","version":5},"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"}