Hypercontractivity for Markov Semigroups

Abstract

We investigate in a systematic way hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non homogeneous diffusions in ${\mathbb{R}}^n$. We provide an explicit construction of a family of Orlicz functions for which we prove that the associated hypercontractivity property is equivalent to a suitable functional inequality.

closed to published version

References in corpus (2)

• Higher Order Coercive Inequalities
• Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in $L^1$