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

作     者：HE Le-ping CHEN Xiao-yu SHANG Xiao-zhou HE Le-ping;CHEN Xiao-yu;SHANG Xiao-zhou

作者机构：Department of Mathematics and Computer Science Jishou University Jishou 416000 China Department of Mathematics and Computer Science Normal College Jishou University Jishou 416000 China 

出 版 物：《Chinese Quarterly Journal of Mathematics》 (数学季刊（英文版）)

年 卷 期：2007年第22卷第1期

页      面：68-74页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Hardy-Hilbert's type inequality Hardy-Littlewood's inequality Hoelder's inequality beta function 

摘      要：In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy 〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.