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  Volume 10, Issue 4, Article 115
Hardy-Hilbert Type Inequalities with Fractional Kernel in $R^n$

    Authors: Mario Krnic, Josip E. Pecaric, Ivan Perić, Predrag Vuković,  
    Keywords: Inequalities, multiple Hilbert's inequality, multiple Hardy-Hilbert's inequality, equivalent inequalities, non-conjugate parameters, gamma function, Selberg's integral, the best possible constant, symmetric-decreasing function, general rearrangement inequality, hypergeometric function.  
    Date Received: 01/07/2009  
    Date Accepted: 18/11/2009  
    Subject Codes:


    Editors: Gord Sinnamon,  

The main objective of this paper is some new special Hilbert-type and Hardy-Hilbert-type inequalities in $mathbf{(R^n)^k}$ with $kgeq 2$ non-conjugate parameters which are obtained by using the well known Selberg's integral formula for fractional integrals in an appropriate form. In such a way we obtain extensions over the whole set of real numbers, of some earlier results, previously known from the literature, where the integrals were taken only over the set of positive real numbers. Also, we obtain the best possible constants in the conjugate case.

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