Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

被引：54

作者：

Artstein-Avidan, S. ^{[2
]}

Klartag, B. ^{[2
]}

Schuett, C. ^{[3
]}

Werner, E. ^{[1
,4
]}

机构：

[1] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

[3] Univ Kiel, Math Inst, D-24105 Kiel, Germany

[4] Univ Lille 1, UFR Math, F-59655 Villeneuve Dascq, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 09期

基金：

美国国家科学基金会;

关键词：

Affine isoperimetric inequality; Logarithmic Sobolev inequality;

D O I：

10.1016/j.jfa.2012.02.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincare inequality for the Gaussian measure. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：4181 / 4204

页数：24

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