应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2011年
1期
38-45
,共8页
高斯测度%Ornstein-Uhlenbeck半群%Ornstein-Uhlenbeck算子
高斯測度%Ornstein-Uhlenbeck半群%Ornstein-Uhlenbeck算子
고사측도%Ornstein-Uhlenbeck반군%Ornstein-Uhlenbeck산자
Gaussian measure%Ornstein-Uhlenbeck semigroup%Ornstein-Uhlenbeck operator
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.
按照Ornstein-Uhlenbeck的思想方法,用Ornstein-Uhlenbeck半群和Ornstein-Uhlenbeck算子的一些重要性質,對Brascamp-Lieb不等式、高斯對數Sobolev不等式、逆Bobkov等週不等式等幾箇重要的幾何與分析不等式給齣瞭另一證明.
안조Ornstein-Uhlenbeck적사상방법,용Ornstein-Uhlenbeck반군화Ornstein-Uhlenbeck산자적일사중요성질,대Brascamp-Lieb불등식、고사대수Sobolev불등식、역Bobkov등주불등식등궤개중요적궤하여분석불등식급출료령일증명.
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.
