Two-weight, weak-type norm inequalities for fractional integrals, Calderon-Zygmund operators

Abstract

We give Ap-type conditions which are sucient for the two-weight, weak-type (p,p) inequalities for fractional integral operators, Calderon-Zygmund operators and commutators. For fractional integral operators, this solves a problem posed by Sawyer and Wheeden (28). At the heart of all of our proofs is an inequality relating the Hardy-Littlewood maximal function and the sharp maximal function which is strongly reminiscent of the good- inequality of Feerman and Stein (13).