Weighted inequalities for the two-dimensional one-sided Hardy-Littlewood maximal function

Abstract

In this work we characterize the pairs of weights (w, v) such that the one-sided Hardy-Littlewood maximal function in dimension two is of weak-type (p, p), 1 ≤ p ≤ ∞, with respect to the pair (w, v). As an application of this result we obtain a generalization of the classic Dunford-Schwartz Ergodic Maximal Theorem for bi-parameter flows of null-preserving transformations.