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2010 Poincaré inequality and the $L^p$ convergence of semi-groups
Patrick Cattiaux, Arnaud Guillin, Cyril Roberto
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Electron. Commun. Probab. 15: 270-280 (2010). DOI: 10.1214/ECP.v15-1559


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) $L^p(\mu)$ spaces for $1 < p < \infty$. We also give the optimal rate of convergence. Part of these results extends to the stationary, not necessarily symmetric situation.


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Patrick Cattiaux. Arnaud Guillin. Cyril Roberto. "Poincaré inequality and the $L^p$ convergence of semi-groups." Electron. Commun. Probab. 15 270 - 280, 2010.


Accepted: 9 June 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1223.26037
MathSciNet: MR2661206
Digital Object Identifier: 10.1214/ECP.v15-1559

Primary: 26D10
Secondary: ‎39B62 , 47D07 , 60G10 , 60J60

Keywords: Poincaré inequality , rate of convergence

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