Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 637397, 10 pages
doi:10.1155/2008/637397
Research Article

On a New Weighted Hilbert Inequality

He Leping,1 Gao Xuemei,2,3 and Gao Mingzhe2

 1Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Hunan Jishou 416000, China
2Department of Mathematics and Computer Science, Normal College of Jishou University, Hunan Jishou 416000, China
3Department of Mathematics, College of Mathematics and Computer Science, Hunan Normal University, Hunan Changsha 410081, China
Received 13 January 2008; Accepted 18 May 2008

Recommended by László Losonczi

Abstract

It is shown that a weighted Hilbert inequality for double series can be established by introducing a proper weight function. Thus, a quite sharp result of the classical Hilbert inequality for double series is obtained. And a similar result for the Hilbert integral inequality is also proved. Some applications are considered.