On the Generalized Ornstein-Uhlenbeck Semigroup
arXiv:1907.13474
Abstract
We give several functional inequalities related to the Ornstein-Uhlenbeck semigroup in the Dunkl differential-difference operators setting. As an application of these inequalities, we derive out a Sobolev-logarithmic and an hypercontractivity properties for this semigroup
some results were not satisfactory