Hardy-Hilbert积分不等式的改进  

A Refinement of Hardy-Hilbert's Integral Inequality

作　　者：沈家梅[1] 高明哲[1] 

机构地区：[1]吉首大学师范学院数学与计算机科学系,湖南吉首416000

出　　处：《大学数学》2008年第4期117-121,共5页College Mathematics

摘　　要：通过引入带参数的指数积分并利用Bernoulli不等式以及改进了的Hlder不等式,对Hardy-Hilbert积分不等式作了有意义改进.特别,当p=2时,得到了经典的Hilbert积分不等式的一个很强的结果.It is shown that a significant refinement of Hardy-Hilbert＇s integral inequality can be built by introducing exponential integral with parameter t and by using Bernoulli＇s inequality as well as improved Holder＇s inequality, In particular, for case p= 2, a sharp result of the classical Hilbert inequality is obtained.

关 键 词：HARDY-HILBERT积分不等式 BERNOULLI不等式 指数积分 HOLDER不等式 权系数 

分 类 号：O178[理学—数学]