A Bakry-Émery criterion for weighted contractivity and $L^2$-Hardy inequalities

Abstract

We show a symmetric Markov diffusion semigroup satisfies a weighted contractivity condition if and only if a $L^2$-Hardy inequality holds, and we give a Bakry-Émery type criterion for the former. We then give some applications.

23 pages, changed title, some changes made according to referee recommendations, to appear in Commun. Contemp. Math

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