Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on
Annales mathématiques Blaise Pascal, Volume 23 (2016) no. 1, pp. 129-140.

In a 2013 paper, the author showed that the convolution of a compactly supported measure on the real line with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). In a 2014 paper, the author gave bounds for the optimal constants in these LSIs. In this paper, we give a simpler, elementary proof of this result.

Dans un article de 2013, l’auteur a montré que la convolution d’une mesure à support compact sur la droite réelle avec une mesure gaussienne satisfait une inégalité de Sobolev logarithmique. Dans un article de 2014, l’auteur a donné des bornes pour les constantes optimales dans ces inégalités de Sobolev logarithmiques. Dans cet article, nous donnons une preuve élémentaire simple de ce résultat.

Published online:
DOI: 10.5802/ambp.357
Classification: 26D10
Keywords: Logarithmic Sobolev inequality, convolutions
David Zimmermann 1

1 Department of Mathematics University of California, San Diego 9500 Gilman Drive La Jolla, CA 92093, USA
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     title = {Elementary proof of logarithmic {Sobolev} inequalities for {Gaussian} convolutions on $\mathbb{R}$},
     journal = {Annales math\'ematiques Blaise Pascal},
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David Zimmermann. Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$. Annales mathématiques Blaise Pascal, Volume 23 (2016) no. 1, pp. 129-140. doi : 10.5802/ambp.357. https://ambp.centre-mersenne.org/articles/10.5802/ambp.357/

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