On the Hilbert Inequality With Weights

Abstract

In this paper, it is shown that a Hilbert-type inequality with weight ω(n) = π − θ √ 2n+1 can be established where θ = 17 20 . As application, a quite sharp result of the Hardy-Littlewood inequality is obtained and some further extensions are obtained.

A Further Generalization of Hardy-Hilbert's Integral Inequality with Parameter and Applications

“…The main purpose of this paper is to establish a new extended Hardy-Hilbert's type inequality, which includes improvements and generalisations of the corresponding results from [2]- [3].…”