Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 572176, 9 pages
Research Article

On a Hilbert-Type Operator with a Class of Homogeneous Kernels

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

Received 15 September 2008; Accepted 20 February 2009

Academic Editor: Patricia J. Y. Wong

Copyright © 2009 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.


By using the way of weight coefficient and the theory of operators, we define a Hilbert-type operator with a class of homogeneous kernels and obtain its norm. As applications, an extended basic theorem on Hilbert-type inequalities with the decreasing homogeneous kernels of λ-degree is established, and some particular cases are considered.