International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 297508, 8 pages
Research Article

On New Extensions of Hilbert's Integral Inequality

He Leping,1 Gao Mingzhe,2 and Zhou Yu2

1Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Jishou Hunan 416000, China
2Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000, China

Received 11 September 2007; Revised 5 November 2007; Accepted 11 December 2007

Academic Editor: Feng Qi

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 some new extensions of Hilbert's integral inequality with parameter λ(λ>1/2) can be established by introducing a proper weight function. In particular, when λ=1, a refinement of Hilbert's integral inequality is obtained. As applications, some new extensions of Widder's inequality and Hardy-Littlewood's inequality are given.