# Lyapunov conditions for Super Poincaré inequalities

@article{Cattiaux2009LyapunovCF, title={Lyapunov conditions for Super Poincar{\'e} inequalities}, author={Patrick Cattiaux and Arnaud Guillin and Feng-Yu Wang and Liming Wu}, journal={Journal of Functional Analysis}, year={2009}, volume={256}, pages={1821-1841} }

## 53 Citations

### Weak Poincaré inequalities for convolution probabilities measures

- MathematicsInfinite Dimensional Analysis, Quantum Probability and Related Topics
- 2019

In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is…

### A Link Between the Log-Sobolev Inequality and Lyapunov Condition

- Mathematics
- 2014

We give an alternative look at the log-Sobolev inequality (LSI in short) for log-concave measures by semigroup tools. The similar idea yields a heat flow proof of LSI under some quadratic Lyapunov…

### Weighted Poincar\'{e} Inequalities for Nonlocal Dirichlet Forms

- Mathematics
- 2012

on L(μV ). Taking ρ(r) = e r with 0 < α < 2 and δ > 0, we get some conclusions for general fractional Dirichlet forms, which can be regarded as a complement of our recent work [13], and an…

### E INEQUALITIES AND HITTING TIMES

- Mathematics
- 2010

Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible…

### Poincare inequality and exponential integrability of the hitting times of a Markov process

- Mathematics
- 2013

Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a…

### Poincaré and Logarithmic Sobolev Inequalities for Nearly Radial Measures

- MathematicsActa Mathematica Sinica, English Series
- 2022

If Poincare inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods:…

### Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry

- Mathematics
- 2008

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as…

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