The Best Constants in Multidimensional Hilbert-Type Inequalities Involving Some Weighted Means Operators

Abstract

In this paper, we establish several multidimensional Hilbert-type inequalities with a homogeneous kernel, involving the weighted geometric and harmonic mean operators in the integral case. The general results are derived for the case of non-conjugate parameters. A special emphasis is dedicated to determining conditions under which the obtained inequalities include the best possible constants on their right-hand sides, which can be established after reduction to the conjugate case. As an application, we consider some particular examples and compare our results with the previously known from the literature.