Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality

Details Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality

2007-12-03

arxiv.org/abs/0712.0235v1

Journal of Functional Analysis 256, 6 (2009) 1821-1841

Mathematics

Probability

Scientific paper

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar\'e inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincar\'e and weak Poincar\'e inequalities was studied in Bakry and al. This approach allows us to recover and extend in an unified way some known criteria in the euclidean case (Bakry-Emery, Wang, Kusuoka-Stroock ...).

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