{"paper":{"title":"$H^\\infty$-calculus for semigroup generators on BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Brian Simanek, Tao Mei, Tim Ferguson","submitted_at":"2017-01-23T20:38:11Z","abstract_excerpt":"We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^\\infty$ has a bounded $H^\\infty(S_\\eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $\\eta>\\pi/2$, provided the semigroup satisfies Bakry-Emry's $\\Gamma_2 $ criterion. Our arguments only rely on the properties of the underlying semigroup and works well in the noncommutative setting. A key ingredient of our argument is a quasi monotone property for the subordinated semigroup $T_{t,\\alpha}=e^{-tL^\\alpha},0<\\alpha<1$, that is proved in the first half of the article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06623","kind":"arxiv","version":5},"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"}