L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains

TL;DR

This paper extends the theory of Ornstein-Uhlenbeck semigroups to non-symmetric cases on open domains, providing new conditions for the domain of the square root of the generator to be a Sobolev space.

Contribution

It introduces new results on analytic non-symmetric Ornstein-Uhlenbeck semigroups and generalizes existing work to broader non-symmetric settings.

Findings

Conditions for the domain of om(\u221a{-L_O}) to be a Sobolev space

Extension of previous symmetric results to non-symmetric cases

New analytic properties of Ornstein-Uhlenbeck semigroups on domains

Abstract

We present some new results on analytic Ornstein-Uhlenbeck semigroups and use them to extend recent work of Da Prato and Lunardi for Ornstein-Uhlenbeck semigroups on open domains O to the non-symmetric case. Denoting the generator of the semigroup by L_O, we obtain sufficient conditions in order that the domain Dom(\sqrt{-L_O}) be a first order Sobolev space.