中文摘要：

按照Ornstein-Uhlenbeck的思想方法,用Ornstein-Uhlenbeck半群和Ornstein-Uhlenbeck算子的一些重要性质,对Brascamp-Lieb不等式、高斯对数Sobolev不等式、逆Bobkov等周不等式等几个重要的几何与分析不等式给出了另一证明.

英文摘要：

In this paper,according to the idea of Ornstein-Uhlenbeck,we apply some important properties of Ornstein-Uhlenbeck semigroup and Ornstein-Uhlenbeck operator,and give another proofs of the Brascamp-Lieb inequalities, the Gaussian logarithmic Sobolev inequality,and the reverse Bobkov isoperimetric inequality.