Poincaré inequality and the Lp convergence of semi-groups

2010/03/03 by Cattiaux, Patrick, Guillin, Arnaud, Roberto, Cyril
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1003.0784

Abstract

We prove that for symmetric Markov processes of diffusion type admitting a "carré du champ", the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) Ł^p(μ) spaces for p∈ (1,+∞). Part of this result extends to the stationary non necessarily symmetric situation.

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