Weighted Inequalities for One-Sided Vector-Valued Maximal Operators with Respect to a Function

Abstract

The purpose of this paper is to find necessary and sufficient conditions on the weight \(w\) for the weak type \(\left( p,p\right) \) with \(1\leq p<+\infty \) and for the strong type \(\left( p,p\right)\) with \(1<p<+\infty \) respect to a measure \(w\,dx\) of the vector-valued one-sided maximal operator \(\left(M_{g}^{+}\right) _{r}\).