article

Title: Some remarks on weighted logarithmic Sobolev inequality

Authors: Patrick Cattiaux, Arnaud Guillin and Li-Ming Wu

Issue: Volume 60 (2011), Issue 6, 1885-1904

Abstract:

$We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux [S.G. Bobkov and M. Ledoux, \textit{Weighted Poincar\'e-type inequalities for Cauchy and other convex measures}, Ann. Probab. \textbf{37} (2009), no. 2, 403--427]. Some consequences are also discussed.$