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

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. © 2006 Elsevier Inc. All rights reserved