Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 28582, 12 pages
Best constants for certain multilinear integral operators
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
Copyright © 2006 Árpád Bényi and Choonghong (Tadahiro) Oh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.