Functional inequalities for some generalised Mehler semigroups

Abstract

We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure $\sigma$, we prove functional integral inequalities with respect to $\sigma$, such as logarithmic Sobolev and Poincar\'{e} type. Consequently, some integrability properties of exponential functions with respect to $\sigma$ are deduced.