On a more accurate half-discrete Hilbert's inequality

Abstract

By using the way of weight coefficients and the idea of introducing parameters and by means of Hadamard's inequality, we give a more accurate half-discrete Hilbert's inequality with a best constant factor. We also consider its best extension with parameters, the equivalent forms, the operator expressions as well as some reverses.

On an Inequality Related to Hilbert's With Laplace Transform

“…Recently, some mathematicians have become interested in what so called half-discrete Hilbert-type inequalities see for instance [5] and [6]. In the left-hand sides of this kind of inequalities we have a "mixture" of summations and integrals with a combination between discrete and continuous variables.…”