On New Extensions of Hilbert's Integral Inequality - He Leping; Gao Mingzhe; Zhou Yu (International Journal of Mathematics and Mathematical Sciences)
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.