{"paper":{"title":"Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Jan Maas, Jan van Neerven","submitted_at":"2009-11-23T08:00:47Z","abstract_excerpt":"Let (P(t)) be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t) = AU(t)dt + dW_H(t), where A is the generator of a C_0-semigroup (S(t)) on a Banach space E, H is a Hilbert subspace of E, and (W_H(t)) is an H-cylindrical Brownian motion. Assuming that (S(t)) restricts to a C_0-semigroup on H, we obtain L^p-bounds for the gradient D_H P(t). We show that if (P(t)) is analytic, then the invariance assumption is fulfilled. As an application we determine the L^p-domain of the generator of (P(t)) explicitly in the case where (S(t)) restricts to a C_0-semigroup on H "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4336","kind":"arxiv","version":3},"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"}