JIPAM
HardyHilbert 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 HardyHilbert's inequality, equivalent inequalities, nonconjugate parameters, gamma function, Selberg's integral, the best possible constant, symmetricdecreasing function, general rearrangement inequality, hypergeometric function. 


Date Received:

01/07/2009 


Date Accepted:

18/11/2009 


Subject Codes: 
26D15.



Editors: 
Gord Sinnamon, 







Abstract: 
The main objective of this paper is some new special Hilberttype and HardyHilberttype inequalities in with nonconjugate 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. ;

This article was printed from JIPAM
http://jipam.vu.edu.au
The URL for this article is:
http://jipam.vu.edu.au/article.php?sid=1171
