International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 297508, 8 pages
doi:10.1155/2008/297508
On new extensions of Hilbert's integral inequality
He Leping1
, Gao Mingzhe2
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
Abstract
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.