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

Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (1): 68-74.

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

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

Received:2003-11-21 Online:2007-03-30 Published:2023-11-13
About author:HE Le-ping(1965-),male,native of Loudi,Hunan,an associate professor of Jishou University, engages in real function theory and ordinary differential equations.

Abstract

Abstract: In this paper,it is shown that Hardy-Hilbert’s integral inequality with parameter is improved by means of a sharpening of Holder’s inequality.A new inequality is established as follows: ... , where R=(S_p(F, h)-S_q(G, h))²,m=min{1/p,1/q}.As application;an extension of Hardy-Littlewood’s inequality is given.

Key words: Hardy-Hilbert's , type , inequality, Hardy-Littlewood's , inequality, Holder's , in- equality, beta , function

CLC Number:

O175.5

HE Le-ping, CHEN Xiao-yu, SHANG Xiao-zhou. An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(1): 68-74.

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

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