| 直线上函数的Banach空间的Poincaré型不等式的变分公式 |
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| 引用本文： | 陈木法. 直线上函数的Banach空间的Poincaré型不等式的变分公式[J]. 数学学报, 2005, 48(2): 209-220. DOI: cnki:ISSN:0583-1431.0.2005-02-001 |
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| 作者姓名： | 陈木法 |
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| 作者单位： | 北京师范大学数学系 北京100875 |
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| 基金项目： | 973项目国家自然科学基金(10121101)教育部博士点专项基金资助项目 |
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| 摘 要： | 基于研究对数Sobolev,Nash和其它泛函不等式的需要,将Poincare不等式 的变分公式拓广到一大类直线上函数的Banach(Orlicz)空间.给出了这些不等式成立 与否的显式判准和显式估计. 作为典型应用,仔细考察了对数Sobolev常数.
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| 关 键 词： | 变分公式 Poincaré不等式 对数Sobolev不等式 Orlicz空间 |
Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line |
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| Mu Fa CHEN. Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line[J]. Acta Mathematica Sinica, 2005, 48(2): 209-220. DOI: cnki:ISSN:0583-1431.0.2005-02-001 |
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| Authors: | Mu Fa CHEN |
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| Affiliation: | Mu Fa CHEN Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined. |
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| Keywords: | Variational formula Poincare inequality Logarithmic Sobolev inequality Orlicz space |
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