Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 192197, 13 pages
doi:10.1155/2009/192197
Research Article

On a Multiple Hilbert-Type Integral Operator and Applications

Qiliang Huang and Bicheng Yang

Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China

Received 19 August 2009; Accepted 9 December 2009

Academic Editor: Wing-Sum Cheung

Copyright © 2010 Qiliang Huang and Bicheng Yang. 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

By using the way of weight functions and the technic of real analysis, a multiple Hilbert-type integral operator with the homogeneous kernel of −λ-degree (λ∈R) and its norm are considered. As for applications, two equivalent inequalities with the best constant factors, the reverses, and some particular norms are obtained.