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Lyapunov conditions for Super Poincaré inequalities

Authors :
Feng-Yu Wang
Liming Wu
Patrick Cattiaux
Arnaud Guillin
Institut de Mathématiques de Toulouse UMR5219 (IMT)
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Laboratoire de Mathématiques Blaise Pascal (LMBP)
Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS)
School of Mathematical Sciences [Beijing] (SMS)
Beijing Normal University (BNU)
Institute of Applied Mathematics
Chinese Academy of Sciences [Beijing] (CAS)
Université Toulouse Capitole (UT Capitole)
Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)
Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3)
Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Source :
Journal of Functional Analysis, Journal of Functional Analysis, Elsevier, 2009, 256 (6), pp.1821-1841. ⟨10.1016/j.jfa.2009.01.003⟩, Journal of Functional Analysis, 2009, 256 (6), pp.1821-1841. ⟨10.1016/j.jfa.2009.01.003⟩
Publication Year :
2009
Publisher :
Elsevier BV, 2009.

Abstract

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or F-Sobolev). The case of Poincaré and weak Poincaré inequalities was studied in [D. Bakry, P. Cattiaux, A. Guillin, Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré, J. Funct. Anal. 254 (3) (2008) 727–759. Available on Mathematics arXiv:math.PR/0703355, 2007]. This approach allows us to recover and extend in a unified way some known criteria in the euclidean case (Bakry and Emery, Wang, Kusuoka and Stroock, …).

Details

ISSN :
00221236 and 10960783
Volume :
256
Database :
OpenAIRE
Journal :
Journal of Functional Analysis
Accession number :
edsair.doi.dedup.....d7f03e09cea8b5a7a5b918b1d2d6dd03
Full Text :
https://doi.org/10.1016/j.jfa.2009.01.003