Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators

We give Ap-type conditions which are sufficient for the two-weight, weak-type (p, p) inequalities for fractional integral operators, Calderón-Zygmund operators and commutators. For fractional integral operators, this solves a problem posed by Sawyer and Wheeden. 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-λ inequality of Fefferman and Stein.Ford FoundationDirección General de Investigación Científica y Técnic