{"paper":{"title":"Hypercontractivity in group von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO"],"primary_cat":"math.OA","authors_text":"Carlos Palazuelos, Javier Parcet, Marius Junge, Mathilde Perrin","submitted_at":"2013-04-21T19:55:37Z","abstract_excerpt":"In this paper, we provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. We will illustrate our method with free groups, triangular groups and finite cyclic groups, for which we shall obtain optimal time hypercontractive $L_2 \\to L_q$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer. Interpolation and differentiation also yield general $L_p \\to L_q$ hypercontrativity for $1 < p \\le q < \\infty$ via logarithmic Sobolev inequalities. Our method admits further applications to other d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5789","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"}