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Hardy-Hilbert积分不等式的改进
引用本文:沈家梅,高明哲.Hardy-Hilbert积分不等式的改进[J].大学数学,2008,24(4).
作者姓名:沈家梅  高明哲
作者单位:吉首大学师范学院,数学与计算机科学系,湖南,吉首,416000
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.

关 键 词:Hardy-Hilbert积分不等式  Bernoulli不等式  指数积分  Hlder不等式  权系数

A Refinement of Hardy-Hilbert's Integral Inequality
SHEN Jia-mei,GAO Ming-zhe.A Refinement of Hardy-Hilbert''s Integral Inequality[J].College Mathematics,2008,24(4).
Authors:SHEN Jia-mei  GAO Ming-zhe
Abstract: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 Hlder's inequality.In particular,for case p=2,a sharp result of the classical Hilbert inequality is obtained.
Keywords:Hardy-Hilbert's inequality  Bernoulli's inequality  exponential integral  Hlder's inequality  weight coefficient
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