Functional Inequalities for Some Generalised Mehler Semigroups.

We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure σ , we prove functional integral inequalities with respect to σ , such as logarithmic Sobolev and Poincaré type. Consequently, some integrability properties of exponential functions with respect to σ are deduced. [ABSTRACT FROM AUTHOR]