| Ornstein-Uhlenbeck半群证明不等式的一些应用 |
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| 引用本文： | 黄卿中,何斌吾. Ornstein-Uhlenbeck半群证明不等式的一些应用[J]. 应用数学与计算数学学报, 2011, 25(1): 38-45 |
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| 作者姓名： | 黄卿中 何斌吾 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 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.
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| 关 键 词： | 高斯测度 Ornstein-Uhlenbeck半群 Ornstein-Uhlenbeck算子 |
Some applications of Ornstein-Uhlenbeck semigroup in solving inequalities |
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| HUANG Qing-zhong,HE Bin-wu. Some applications of Ornstein-Uhlenbeck semigroup in solving inequalities[J]. Communication on Applied Mathematics and Computation, 2011, 25(1): 38-45 |
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| Authors: | HUANG Qing-zhong HE Bin-wu |
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| Affiliation: | HUANG Qing-zhong,HE Bin-wu (College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | 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. |
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| Keywords: | Gaussian measure Ornstein-Uhlenbeck semigroup Ornstein-Uhlenbeck operator |
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