ON A NON-STANDARD CHARACTERIZATION OF THE Ap CONDITION

The classical Muckenhoupt Ap condition is necessary and sufficient for the boundedness of the maximal operator M on Lp(w) spaces. In this paper we obtain another characterization of the Ap condition. As a result, we show that some strong versions of the weighted Lp(w) Coifman–Fefferman and Fefferman–Stein inequalities hold if and only if w ∈ Ap. We also give new examples of Banach function spaces X such that M is bounded on X but not bounded on the associate space X′.