Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces
Marco Fuhrman · Stochastic Analysis and Applications · 1998
We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup. We show by examples that in our setting logarithmic Sobolev inequalities do not hold in general