Hilbert-type inequalities and related operators with homogeneous kernel of degree 0

Abstract

In this paper we provide an unified approach to the Hilbert-type inequalities with homogeneous kernel of degree 0 and certain weight functions. As an application, we define the related Hilbert-type operators and analyze their norms. In the case of conjugate exponents, we obtain the best possible constants involved in the right-hand sides of derived inequalities, and norms of the Hilbert-type operators as well. Finally, we consider some special choices of homogeneous kernels and parameters.