Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 812636, 10 pages
doi:10.1155/2010/812636
Research Article

On a New Hilbert-Hardy-Type Integral Operator and Applications

Xingdong Liu1 and Bicheng Yang2

1Department of Mathematics, Zhaoqing University, Guangdong, Zhaoqing 526061, China
2Department of Mathematics, Guangdong Institute of Education, Guangdong, Guangzhou 510303, China

Received 7 September 2010; Accepted 26 October 2010

Academic Editor: Sin E. Takahasi

Copyright © 2010 Xingdong Liu 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 applying the way of weight functions and a Hardy's integral inequality, a Hilbert-Hardy-type integral operator is defined, and the norm of operator is obtained. As applications, a new Hilbert-Hardy-type inequality similar to Hilbert-type integral inequality is given, and two equivalent inequalities with the best constant factors as well as some particular examples are considered.