[Une preuve élémentaire des inégalités de Sobolev logarithmiques pour des convolutions gaussiennes sur ]
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.
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.
Keywords: Logarithmic Sobolev inequality, convolutions
Mot clés : inégalités de Sobolev logarithmiques, circonvolutions
@article{AMBP_2016__23_1_129_0,
author = {Zimmermann, David},
title = {Elementary proof of logarithmic {Sobolev} inequalities for {Gaussian} convolutions on $\mathbb{R}$},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {129--140},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {23},
number = {1},
year = {2016},
doi = {10.5802/ambp.357},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/ambp.357/}
}
TY - JOUR
AU - Zimmermann, David
TI - Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$
JO - Annales mathématiques Blaise Pascal
PY - 2016
SP - 129
EP - 140
VL - 23
IS - 1
PB - Annales mathématiques Blaise Pascal
UR - http://archive.numdam.org/articles/10.5802/ambp.357/
DO - 10.5802/ambp.357
LA - en
ID - AMBP_2016__23_1_129_0
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Zimmermann, David. Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 1, pp. 129-140. doi : 10.5802/ambp.357. http://archive.numdam.org/articles/10.5802/ambp.357/
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