A reverse Hardy–Hilbert-type integral inequality involving one derivative function

In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

A Hilbert Integral-Type Inequality with Parameters

A Hilbert-type integral inequality with parametersαand(α,λ>0)can be established by introducing a nonhomogeneous kernel function. And the constant factor is proved to be the best possible. And then some important and especial results are enumerated. As applications, some equivalent forms are studied.

Generalized Hilbert integral operators on the Herz spaces

This paper gives some necessary and sufficient conditions for the generalized Hilbert integral operators to be bounded on the Herz spaces. The corresponding new operator norm inequalities are obtained.