Stochastic maximal Lp-regularity

In this article we prove a maximal Lp-regularity result for stochastic convolutions, which extends Krylov’s basic mixed Lp(Lq)-inequality for the Laplace operator on ℝd to large classes of elliptic operators, both on ℝd and on bounded domains in ℝd with various boundary conditions. Our method of proof is based on McIntosh’s H∞-functional calculus, R-boundedness techniques and sharp Lp(Lq)-square function estimates for stochastic integrals in Lq-spaces. Under an additional invertibility assumption on A, a maximal space–time Lp-regularity result is obtained as well.

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