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