An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application

被引：0
|
作者：
HE Le-ping~1 CHEN Xiao-yu~2 SHANG Xiao-zhou~2 (1.Department of Mathematics and Computer Science
2.Department of Mathematics and Computer Science
机构：
来源：
数学季刊 | 2007年 / 01期
关键词：
Hardy-Hilbert’s type inequality; Hardy-Littlewood’s inequality; Hlder’s inequality; beta function;
D O I：
暂无
中图分类号：
O175.5 [积分方程];
学科分类号：
摘要：
In this paper,it is shown that Hardy-Hilbert’s integral inequality with parameter is improved by means of a sharpening of Hlder’s inequality.A new inequality is established as follows: （integral fromαto∞）(integral fromαto∞)(f（x）g（y）/（x+y+2β）)dxdy <(π/sin（π/p）){（integral fromαto∞）f（x）dx}·{（integral fromαto∞）g（x）dx}·（1-R）, where R=(S（F,h）-S（G,h）),m=min{1/p,1/q}.As application;an extension of Hardy-Littlewood’s inequality is given.
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页码：68 / 74
页数：7
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