{"paper":{"title":"On the optimality of the hypercontractivity of the complex Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Pellegrino, G. A. Mu\\~noz-Fern\\'andez, J. B. Seoane-Sep\\'ulveda, J. R. Campos","submitted_at":"2013-01-08T14:08:13Z","abstract_excerpt":"The main motivation of this paper is the following open problem: Is the hypercontractivity of the \\emph{complex} polynomial Bohnenblust--Hille inequality an optimal result? We show that the solution to this problem has a close connection with the searching of the optimal constants for the \\emph{real} polynomial Bohnenblust--Hille inequality. So we are lead to a detailed study of the hypercontractivity constants for real scalars. In fact we study two notions of constants of hypercontractivity: absolute ($H_{a,\\mathbb{R}}$) and asymptotic ($H_{\\infty,\\mathbb{R}}$). Among other results, our estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1539","kind":"arxiv","version":4},"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"}