| Poincaré Inequalities on a Countable Set E and Ω={x:0≤x_i≤a, i=1,2,…,n} |
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| 引用本文： | 陈文英.Poincaré Inequalities on a Countable Set E and Ω={x:0≤x_i≤a, i=1,2,…,n}[J].西南交通大学学报(英文版),2005,13(1). |
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| 作者姓名： | 陈文英 |
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| 作者单位： | Department of |
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| 摘 要： | IntroductionPoincaréinequalitiesarewidelyappliedinmanyfieldssuchasstochasticanalysis,functionalanalysisandeigenvalueestimate. AlotofresultsaboutPoincaréinequalitieshavebeenobtained1-4], mostofthemwerebasedontheboundeddomaininndimen sionalEuclideanspace…
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| 关 键 词： | Countable set Poincaré inequalities Weight function |
Poincaré Inequalities on a Countable Set E and Ω={x:0≤xi≤a, i=1,2,...,n} |
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| CHEN Wenying.Poincaré Inequalities on a Countable Set E and Ω={x:0≤xi≤a, i=1,2,...,n}[J].Journal of Southwest Jiaotong University,2005,13(1). |
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| Authors: | CHEN Wenying |
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| Abstract: | In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincaré inequalities (f-μ(f))nB≤cD(f, f) is presented to expand the research and application scope. As to inequalities for Ω={x:0≤xi≤a, i=1,2,...,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincaré inequalities is presented. |
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| Keywords: | Countable set Weight function |
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