Functional Inequalities for Convolution Probability Measures

Abstract

Let $\mu$ and $\nu$ be two probability measures on ${\mathbb{R}}^d$, where $μ(\d x)= \e^{-V(x)}\d x$ for some $V\in C^1({\mathbb{R}}^d)$. Explicit sufficient conditions on $V$ and $\nu$ are presented such that $\mu \ast \nu$ satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, the recent results on the log-Sobolev inequality derived in \cite{Z} for convolutions of the Gaussian measure and compactly supported probability measures are improved and extended.

18 pages

References in corpus (3)

• Weak Poincaré Inequality for Convolution Probability Measures
• Perturbations of Functional Inequalities for Lévy Type Dirichlet Forms
• An extension of the Beckner's type Poincaré inequality to convolution measures on abstract Wiener spaces

Cited by in corpus (3)

• Weak Poincaré Inequality for Convolution Probability Measures
• An extension of the Beckner's type Poincaré inequality to convolution measures on abstract Wiener spaces
• Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$