Poincaré and Logarithmic Sobolev Inequalities for Nearly Radial Measures

被引：0
|
作者：
Patrick CATTIAUX [1 ]
Arnaud GUILLIN [2 ]
Li Ming WU [2 ]
机构：
[1] Institut de Mathématiques de Toulouse,CNRS UMR 5219,Université Paul Sabatier
[2] Laboratoire de Mathématiques Blaise Pascal,CNRS UMR 6620,Université Clermont-Auvergne
来源：
ActaMathematicaSinica,EnglishSeries | 2022年 / 08期
关键词：
D O I：
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中图分类号：
O174.12 [测度论];
学科分类号：
摘要：
Poincaré inequality has been studied by Bobkov for radial measures, but few are known about the logarithmic Sobolev inequality in the radial case. We try to fill this gap here using different methods: Bobkov’s argument and super-Poincaré inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee–Vempala in the log-concave bounded case are refined for radial measures.
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页码：1377 / 1398
页数：22
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