Hardy’s inequalities and integral operators on Herz-Morrey spaces

We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.

A sharper form of half-discrete Hilbert inequality related to Hardy inequality

We introduce some new sharper forms of the half-discrete Hilbert inequality which are connected to the Hardy inequality.

Generalization of Hilbert Inequality with Some Parameters

In this paper, by introducing some parameters and estimating the weight coefficients, some new inequalities are established. All results of Hilbert, Hardy and Yang are considered as special cases of the new given inequalities.

On a sharper form of half-discrete Hilbert inequality

In this paper we introduce a general inequality by using the half-discrete Hilbert inequality. As an application we give a sharper form of the half-discrete Hilbert inequality and some carlson's type inequalities.

A More Accurate Half-Discrete Hilbert Inequality with a Nonhomogeneous Kernel

By using the way of weight functions and the idea of introducing parameters, a more accurate half-discrete Hilbert inequality with a nonhomogeneous kernel and a best constant factor is presented. We also consider its best extension with the parameters, the equivalent forms, and the operator expressions as well as some reverses.