{"paper":{"title":"Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Diogo Diniz, Gustavo Mu\\~noz-Fern\\'andez, Juan B. Seoane-Sep\\'ulveda","submitted_at":"2011-11-14T15:48:24Z","abstract_excerpt":"The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer $N$ and every $m$-linear mapping $T:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow \\mathbb{R}$ one has (\\sum\\limits_{i_{1},...,i_{m}=1}^{N}|T(e_{i_{^{1}}},...,e_{i_{m}})|^{\\frac{2m}{m+1}})^{\\frac{m+1}{2m}}\\leq C_{m}\\VertT\\Vert, for some positive constant $C_{m}$. Since then, several authors obtained upper estimates for the values of $C_{m}$. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for $C_{m}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3253","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"}