Sobolev inequalities for probability measures on the real line
Sobolev inequalities for probability measures on the real line
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DOI：
10.4064/sm159-3-9
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发表时间：
2003
影响因子：
0.8
通讯作者：
F. Barthe;C. Roberto
中科院分区：
文献类型：
--
作者：
F. Barthe;C. Roberto
本文给出了真实的直线上满足Sobolev不等式的概率测度的一个刻划。我们的出发点是一个更简单的方法来Bobkov-Götze特征的措施，满足对数Sobolev不等式。作为该判据的应用，给出了指数测度的Lata-Oleszkiewicz不等式的一个软证明，并描述了线上具有相同性质的测度.新的集中不等式的产品措施如下。
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–Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała–Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.