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

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

机构地区：[1]Department of Mathematics and Computer Science, Jishou University, Jishou 416000, China [2]Department of Mathematics and Computer Science, Normal College, Jishou University, Jishou 416000, China

出　　处：《Chinese Quarterly Journal of Mathematics》2007年第1期68-74,共7页数学季刊（英文版）

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.

关 键 词：Hardy-Hilbert＇s type inequality Hardy-Littlewood＇s inequality Hoelder＇s inequality beta function 

分 类 号：O178[理学—数学]