关于Hlder不等式  

On Hlder Inequality

作　　者：何瑞强[1] 

机构地区：[1]忻州师范学院,山西忻州034000

出　　处：《甘肃联合大学学报（自然科学版）》2012年第3期19-21,共3页Journal of Gansu Lianhe University :Natural Sciences

摘　　要：著名的Hlder不等式在数学分析、调和分析、泛函分析以及偏微分方程等学科的研究中发挥着重要作用.该不等式不仅使用技巧灵活,而且得到的结果极其深刻.本文首先在可测函数论的基础上,给出Hlder不等式的一种新的证明方法,然后利用数学归纳法导出Hlder不等式的推广形式,最后应用Hlder不等式得出两个重要结论,为该不等式在更广数学领域的研究和应用奠定了基础.Famous Holder inequality plays an important role in the study of some disciplines such as mathematical analysis, harmonic analysis, functional analysis and partial differential equations. Not only its tips for using are flexibly, but also the results are very impressive. In this paper,a new method to prove Holder inequality on the basis of measurable functions was given. And generalized Holder inequality is given using mathematical induction forms. Last two important conclusions based on Holder inequality were got. These eonelusions lays the foundation for the equality＇s researches and applica- tions in the wider mathematics areas.

关 键 词：Hlder不等式 可测函数 共轭指数 

分 类 号：O174.1[理学—数学]