On a New Class of Hardy-type Inequalities

Abstract

In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy, Hardy-Hilbert, Hardy-Littlewood-Pólya, and Pólya-Knopp inequalities as well as of Godunova’s and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.