Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 82138, 10 pages
doi:10.1155/2007/82138
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

Recommended by Ram N. Mohapatra

Abstract

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.