Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality

2011/06/02 by Fabrice Baudoin, Baudoin, Fabrice, Michel Bonnefont +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1106.0491

Minor revision of the previous version

arxiv created 2011/11/08 · arxiv updated 2011/11/10

Abstract

Let \M be a smooth connected manifold endowed with a smooth measure μ and a smooth locally subelliptic diffusion operator L which is symmetric with respect to μ. We assume that L satisfies a generalized curvature dimension inequality as introduced by Baudoin-Garofalo \citeBG1. Our goal is to discuss functional inequalities for μ like the Poincaré inequality, the log-Sobolev inequality or the Gaussian logarithmic isoperimetric inequality.

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