{"paper":{"title":"The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Andreas Defant, Joaquim Ortega-Cerd\\`a, Kristian Seip, Leonhard Frerick, Myriam Ouna\\\"ies","submitted_at":"2009-04-23T05:32:57Z","abstract_excerpt":"The Bohnenblust--Hille inequality says that the $\\ell^{\\frac{2m}{m+1}}$-norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\\C^n$ is bounded by $\\| P\\|_\\infty$ times a constant independent of $n$, where $\\|\\cdot \\|_\\infty$ denotes the supremum norm on the polydisc $\\D^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust--Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\\D^n$ behaves asymptotically a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3540","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"}