No abstract

No abstract

No abstract

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 R d to large classes of elliptic operators, both on R d and on bounded domains in R d with various boundary conditions. Our method of proof is based on McIntosh's H ∞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 L p -regularity result is obtained as well.

No abstract