Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 637397, 10 pages
On a New Weighted Hilbert Inequality
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
Academic Editor: László Losonczi
Copyright © 2008 He Leping 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.
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.