Hypercontractivity for Markov semi-groups
Résumé
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. Connections between our results and the Talagrand Conjecture on the regularization effect of the Ornstein-Uhlenbeck semi-group in $\mathbb{L}_1$ are also discussed.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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