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  Volume 7, Issue 1, Article 30
An Extended Hardy-Hilbert Inequality and Its Applications

    Authors: Weijian Jia, Mingzhe Gao,  
    Keywords: Power-exponent function, Weight function, Hardy-Hilbert's integral inequality, Hardy-Littlewood's integral inequality.  
    Date Received: 17/02/04  
    Date Accepted: 10/11/05  
    Subject Codes:


    Editors: Lubos Pick,  

In this paper, it is shown that an extended Hardy-Hilbert's integral inequality with weights can be established by introducing a power-exponent function of the form $ ax^{1 + x}(a> 0,x in [0, + infty ))$, and the coefficient $ frac{pi }{left( a right)^{1/q} left( b right)^{1/p}sin pi/p}$ is shown to be the best possible constant in the inequality. In particular, for the case $ p = 2$, some extensions on the classical Hilbert's integral inequality are obtained. As applications, generalizations of Hardy-Littlewood's integral inequality are given.

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