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

Wuyi Zhong

 Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China
Received 24 March 2008; Accepted 19 May 2008

Recommended by Ondrej Dosly

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.