Pachpatte离散不等式的一个推广  

Generalizations of Pachpatte's Discrete Inequality

作　　者：黄裕建[1] 

机构地区：[1]广东轻工职业技术学院经济系,广州510300

出　　处：《重庆师范大学学报（自然科学版）》2013年第4期98-102,共5页Journal of Chongqing Normal University:Natural Science

基　　金：广东省教育科学"十一五"规划资助项目(No.2010tjkl37)

摘　　要：本文主要研究了Pachpatte不等式的推广及其类似不等式,也就是经典的Hilbert不等式的变式。通过引进-λ齐次函数K(x,y)和两对共轭指数(p,q),(r,s),(1/p)+(1/p)=1,(1/r)+(1/s)=1,经过巧妙配方,再运用一些经典的不等式(例如Hlder不等式、Young不等式与Jensen不等式)技巧和一定的实分析方法来估算权函数,建立了一系列Pach-patte离散不等式的推广及类似形式,包括非负凸、次可乘的可测实值函数下的各种不等式.该结论综合运用了Hilbert不等式和Pachpatte不等式的推演技巧,将以前不含共轭指数或只含一对共轭指数的Pachpatte不等式推广到含两对共轭指数与参量化的不等式,统一了部分已有文献的研究成果,使Pachpatte不等式的研究上升到一个更高的层次。作为应用,对齐-λ次函数K(x,y)取了2个特殊的函数得到了一些有趣的不等式。The present paper is devoted to study the Pachpatte＇s inequality and the similar inequality,which is the variant of classical Hilbert inequality.By introducing the homogeneous function K（x,y） of-λdegree and two pairs of conjugate exponents（p,q）,（r,s）,（1/p） ＋（1/p） =1,（1/r） ＋（1/s） =1,by the proper identical transformation,and then using techniques of several classical inequalities（e.g.Hlder＇s inequality,Young＇s inequality and Jensen＇s inequality） and methods of real analysis to estimate the weight function,a series of Pachpatte＇s discrete inequalities and similar forms are obtained,which included a variety of inequality under the non-negative convex sub-multiplicative measurable real-valued function.This conclusion is the integrated use of the deduction of Hilbert＇s inequality and Pachpatte＇s inequality,putting non-conjugated exponents or only one pair of conjugate exponents of Pachpatte＇s inequality previously into the inequality of two pairs of conjugate exponents and multi-parameter,which unified the research of some literature,this makes the study of Pachpatte＇s inequality to rise to a higher level.As applications,we take two special functions of the homogeneous function K（x,y）,and some interesting inequalities are given.

关 键 词：HOLDER不等式 YOUNG不等式 JENSEN不等式 

分 类 号：O178[理学—数学]