{"paper":{"title":"The L^p-Poincar\\'e inequality for analytic Ornstein-Uhlenbeck operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jan van Neerven","submitted_at":"2014-02-13T15:44:33Z","abstract_excerpt":"Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure \\mu_\\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\\'e inequality \\n f - \\overline f\\n_{L^p(E,\\mu_\\infty)} \\le \\n D_H f\\n_{L^p(E,\\mu_\\infty)} holds for all 1<p<\\infty. Here \\overline f denotes the average of f "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3185","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"}