International Journal of Mathematics and Mathematical Sciences (Jan 2008)
On New Extensions of Hilbert's Integral Inequality
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.
