TWO WEIGHT INEQUALITIES FOR ITERATED COMMUTATORS WITH CALDERON-ZYGMUND OPERATORS

摘要

Given a Calderon-Zygmund operator T, a classic result of Coifman, Rochberg and Weiss relates the norm of the commutator [b, T] with the BMO norm of b. We focus on a weighted version of this result, obtained by Bloom and later generalized by Lacey and the authors, which relates parallel to[b, T] : L-p (R-n; mu) - L-p (R-n; lambda)parallel to to the norm of b in a certain weighted BMO space determined by A(p) weights mu and lambda. We extend this result to higher iterates of the commutator and recover a one-weight result of Chung, Pereyra and Perez in the process.