Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 82138, 10 pages
Research Article

Hilbert's Type Linear Operator and Some Extensions of Hilbert's Inequality

Yongjin Li,1 Zhiping Wang,2 and Bing He3

1Institute of Logic and Cognition, Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
2Department of Mathematics, Guangdong University of Finance, Zhaoqing Campus, Zhaoqing 526060, China
3Department of Mathematics, Guangdong Education College, Guangzhou 510303, China

Received 17 April 2007; Accepted 3 October 2007

Academic Editor: Ram N. Mohapatra

Copyright © 2007 Yongjin Li et al. 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.


The norm of a Hilbert's type linear operator T:L2(0,)L2(0,) is given. As applications, a new generalizations of Hilbert integral inequality, and the result of series analogues are given correspondingly.