Weighted Nash Inequalities

作者: Dominique Bakry , François Bolley , Ivan Gentil , Patrick Maheux

DOI: 10.4171/RMI/695

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摘要: Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this paper …

参考文章(30)
Laurent Saloff-Coste, Sobolev Inequalities in Familiar and Unfamiliar Settings Springer, New York, NY. pp. 299- 343 ,(2009) , 10.1007/978-0-387-85648-3_11
Dominique Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes Springer, Berlin, Heidelberg. pp. 1- 114 ,(1994) , 10.1007/BFB0073872
S. G. Bobkov, Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures Annals of Probability. ,vol. 27, pp. 1903- 1921 ,(1999) , 10.1214/AOP/1022874820
E. A. Carlen, S. Kusuoka, D. W. Stroock, Upper bounds for symmetric Markov transition functions Annales De L Institut Henri Poincare-probabilites Et Statistiques. ,vol. 23, pp. 245- 287 ,(1986) , 10.21236/ADA170010
Cécile Ané, Grégory Scheffer, Ivan Gentil, Cyril Roberto, Sébastien Blachère, Pierre Fougères, Djalil Chafaï, Florent Malrieu, Sur les inégalités de Sobolev logarithmiques Société Mathématique de France. ,(2000)
Benjamin Muckenhoupt, Hardy's inequality with weights Studia Mathematica. ,vol. 44, pp. 31- 38 ,(1972) , 10.4064/SM-44-1-31-38
Rafał Latała, Krzysztof Oleszkiewicz, Between Sobolev and Poincaré Lecture Notes in Mathematics. pp. 147- 168 ,(2000) , 10.1007/BFB0107213
Dominique Bakry, Franck Barthe, Patrick Cattiaux, Arnaud Guillin, A simple proof of the Poincaré inequality for a large class of probability measures Electronic Communications in Probability. ,vol. 13, pp. 60- 66 ,(2008) , 10.1214/ECP.V13-1352
Thierry Coulhon, Ultracontractivity and Nash Type Inequalities Journal of Functional Analysis. ,vol. 141, pp. 510- 539 ,(1996) , 10.1006/JFAN.1996.0140
Dominique Bakry, Patrick Cattiaux, Arnaud Guillin, Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré Journal of Functional Analysis. ,vol. 254, pp. 727- 759 ,(2008) , 10.1016/J.JFA.2007.11.002