Some remarks on weighted logarithmic Sobolev inequality

2010/05/21 by Patrick Cattiaux, Arnaud Guillin, Cattiaux, Patrick +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1005.3908

arxiv created 2010/05/21 · arxiv updated 2010/07/26

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. Some consequences are also discussed.

Related

• Optimal Weighted Poincaré and Log-Sobolev Inequalities for Cauchy Measures
• Logarithmic Sobolev inequality revisited
• Another approach to the equality case of the sharp logarithmic Sobolev inequality
• Sharp Logarithmic Sobolev and related inequalities with monomial weights
• Logarithmic Sobolev inequalities for generalised Cauchy measures