Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 130958, 12 pages
doi:10.1155/2009/130958
Research Article

Multidimensional Hilbert-Type Inequalities with a Homogeneous Kernel

Predrag Vuković

Faculty of Teacher Education, University of Zagreb, Savska cesta 77, 10000 Zagreb, Croatia

Received 11 July 2009; Revised 10 November 2009; Accepted 18 November 2009

Academic Editor: Radu Precup

Copyright © 2009 Predrag Vuković. 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.

Abstract

We consider the Hilbert-type inequalities with nonconjugate parameters. The obtaining of the best possible constants in the case of nonconjugate parameters remains still open. Our generalization will include a general homogeneous kernel. Also, we obtain the best possible constants in the case of conjugate parameters when the parameters satisfy appropriate conditions. We also compare our results with some known results.