Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups

Cyril Roberto (1) , Boguslaw Zegarlinski (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Department of Mathematics [Imperial College London]

We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such inequalities to hold and discuss relations between various classes of inequalities.

Mots clés: Coercive Inequalities; infinite dimensions; decay to equilibrium

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Cyril Roberto, Boguslaw Zegarlinski. Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups. 2006. ⟨hal-00115436⟩