A New Characterization of the Hardy and Its Limit Pólya-Knopp Inequality for Decreasing Functions

Abstract

In this paper we present and prove a new alternative weight characterization for the Hardy inequality for decreasing functions. We also give an alternative approach to the characterization of the Hardy inequality using a fairly new equivalence theorem. In fact, this result shows that there are infinitely many possibilities to characterize the considered Hardy inequality for decreasing functions. We also state the corresponding weight characterization for the Polya-Knopp inequality for decreasing functions.