{"paper":{"title":"Stochastic maximal $L^p$-regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Jan van Neerven, Lutz Weis, Mark Veraar","submitted_at":"2010-04-08T11:15:10Z","abstract_excerpt":"In this article we prove a maximal $L^p$-regularity result for stochastic convolutions, which extends Krylov's basic mixed $L^p(L^q)$-inequality for the Laplace operator on ${\\mathbb{R}}^d$ to large classes of elliptic operators, both on ${\\mathbb{R}}^d$ and on bounded domains in ${\\mathbb{R}}^d$ with various boundary conditions. Our method of proof is based on McIntosh's $H^{\\infty}$-functional calculus, $R$-boundedness techniques and sharp $L^p(L^q)$-square function estimates for stochastic integrals in $L^q$-spaces. Under an additional invertibility assumption on $A$, a maximal space--time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1309","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"}