Weighted and vector-valued inequalities for one-sided maximal functions

Abstract

In this paper, we study weighted and vector-valued inequalities for one-sided maximal functions. In particular, we give a new proof of lr-valued extension of weighted Lp-inequalities for one-sided maximal functions. In the process, we prove an analogue of the well-known Fefferman–Stein’s weighted lemma in the context of one-sided maximal functions. Further, we also study lr-valued extension of the lemma.