Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 28582, 12 pages
doi:10.1155/JIA/2006/28582

Best constants for certain multilinear integral operators

Árpád Bényi1 and Choonghong (Tadahiro) Oh2

 1Department of Mathematics, 516 High Street, Western Washington University, Bellingham 98225-9063, WA, USA
2Department of Mathematics and Statistics, Lederle GRT, University of Massachusetts, Amherst 01003-9305, MA, USA
Received 7 December 2004; Revised 8 March 2005; Accepted 27 March 2005

Abstract

We provide explicit formulas in terms of the special function gamma for the best constants in nontensorial multilinear extensions of some classical integral inequalities due to Hilbert, Hardy, and Hardy-Littlewood-Pólya.