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Lyapunov conditions for Super Poincaré inequalities
- 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, …).
- Subjects :
- Lyapunov function
Pure mathematics
Poincaré inequality
Markov process
Super Poincaré inequalities
01 natural sciences
010104 statistics & probability
symbols.namesake
Euclidean geometry
Ergodic theory
[MATH]Mathematics [math]
0101 mathematics
Logarithmic Sobolev inequalities
ComputingMilieux_MISCELLANEOUS
Lyapunov functions
Mathematics
010102 general mathematics
Mathematical analysis
46E35 35A25 46N30 60J35 60J60
Poincaré inequalities
Sobolev space
Rate of convergence
Ergodic processes
Poincaré conjecture
symbols
Analysis
Subjects
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