Weak weighted inequalities for a dyadic one-sided maximal function in $ \mathbb {R}^{n}$

Abstract

In this note we introduce a dyadic one-sided maximal function defined as formula math. where Q + is a certain cube associated with the dyadic cube Q and f ∈ L 1 loc (R n ). We characterize the pair of weights (w,v) for which the maximal operator M +,d applies L p (v) into weak-L p (w) for 1 ≤ p < oo.