Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 917392, 12 pages
doi:10.1155/2008/917392
Research Article
The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of −λ-Degree
Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China
Received 24 March 2008; Accepted 19 May 2008
Academic Editor: Ondrej Dosly
Copyright © 2008 Wuyi Zhong. 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 introducing an integral operator, a norm with a weight function, and two pairs of conjugate exponents, we find the conditions for the Hilbert-type integral inequalities with a homogeneous kernel of −λ-degree. We also prove that the constant factors in the inequalities are all the best possible. As the particular situations, some new inequalities with a homogeneous kernel and their other two forms are given. We extend some previous results.