Poincaré inequality and the Lp convergence of semi-groups
Cattiaux, Patrick · Guillin, Arnaud · Roberto, Cyril
Original · EN
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) Łᵖ(μ) spaces for p∈ (1,+∞). Part of this result extends to the stationary non necessarily symmetric situation.
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