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Poincaré inequality and the $L^p$ convergence of semi-groups

   
@article{ECP1559,
	author = {Patrick Cattiaux and Arnaud Guillin and Cyril Roberto},
	title = {Poincaré inequality and the $L^p$ convergence of semi-groups},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {Poincaré inequality, rate of convergence},
	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) $L^p(\mu)$ 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.},
	pages = {no. 25, 270-280},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1559},    
        url = {http://ecp.ejpecp.org/article/view/1559}}