Poincaré inequality and the Lp convergence of semi-groups
Résumé
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 $p\in (1,+\infty)$. Part of this result extends to the stationary non necessarily symmetric situation.
Origine | Fichiers produits par l'(les) auteur(s) |
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