Title: Commutators in the two-weight setting

Abstract:  In a foundational paper, Coifman, Rochberg and Weiss relate the norm of the commutator [b, T], where T is a Calderon-Zygmund operator, with the BMO norm of b. In this talk we explore a recent weighted version of this result. Specifically, we study the case when the commutator acts between two different weighted L^p spaces. A first result in this direction was first given by Bloom in 1985, for the Hilbert transform. We discuss an extension of Bloom’s result to all Calderon-Zygmund operators, using dyadic methods.