New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions

Abstract

In this note we give a simple proof of the characterization of the weights for which the one-sided Hardy-Littlewood maximal functions apply L p ( V ) {L^p}(V) into weak- L p ( U ) {L^p}(U) and a direct proof of the characterization of the weights for which the one-sided Hardy-Littlewood maximal functions apply L p ( W ) {L^p}(W) into L p ( W ) {L^p}(W) .