Sobolev inequalities for probability measures on the real line

被引：74

作者：

Barthe, F

Roberto, C

机构：

[1] Univ Marne La Vallee, UMR 8050, CNRS, Lab Anal & Math Appl, F-77454 Marne La Vallee 2, France

[2] Univ Paris 12, UMR 8050, CNRS, Lab Anal & Math Appl, F-77454 Marne La Vallee, France

来源：

STUDIA MATHEMATICA | 2003年 / 159卷 / 03期

关键词：

Sobolev inequalities; concentration;

D O I：

10.4064/sm159-3-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Gotze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latala-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.

引用

页码：481 / 497

页数：17

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[Anonymous], 2000, Lecture Notes in Math.