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


 
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1. Title Title of document Poincaré inequality and the $L^p$ convergence of semi-groups
 
2. Creator Author's name, affiliation, country Patrick Cattiaux; Institut de Mathématiques de Toulouse
 
2. Creator Author's name, affiliation, country Arnaud Guillin; Université Blaise Pascal
 
2. Creator Author's name, affiliation, country Cyril Roberto; Universités de Paris Est Marne la Vallée et de Paris 12-Val-de-Marne
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Poincaré inequality, rate of convergence
 
3. Subject Subject classification 26D10, 39B62, 47D07, 60G10, 60J60
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-06-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1559
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1559
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
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