The weighted Hardy’s inequality for nonincreasing functions

Abstract

The purpose of this paper is to give an alternative proof of recent results of M. Arino and B. Muckenhoupt [1] and E. Sawyer [8], concerning Hardy’s inequality for nonincreasing functions and related applications to the boundedness of some classical operators on general Lorentz spaces. Our approach will extend the results of [1,8] to the values of the parameters which are inaccessible by the methods of these papers.