{"paper":{"title":"A note on the hypercontractivity of the polynomial Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino","submitted_at":"2012-12-29T23:13:48Z","abstract_excerpt":"For $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ and $m$ a positive integer, we remark that there is a constant $C$ so that, for all $r\\in\\lbrack1,\\frac {2m}{m+1}],$ the supremum of the ratio between the $\\ell_{r}$ norm of the coefficients of any nonzero $m$-homogeneous polynomial $P:\\ell_{\\infty}% ^{n}(\\mathbb{K}) \\rightarrow\\mathbb{K}$ and its supremum norm is dominated by $C^{m}\\cdot n^{(\\frac{m}{r}-\\frac{m+1}{2})}$ and, moreover, we prove that the exponent $\\frac{m}{r}-\\frac{m+1}{2}$ is optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6672","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"}