Poincaré inequality and the Lp convergence of semi-groups

Details Poincaré inequality and the Lp convergence of semi-groups Poincaré inequality and the Lp convergence of semi-groups

2010-03-03

arxiv.org/abs/1003.0784v2

Mathematics

Probability

Scientific paper

We prove that for symmetric Markov processes of diffusion type admitting a
"carr\'e du champ", the Poincar\'e 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.

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