Upper bound for multi-parameter iterated commutators

Abstract

We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón-Zygmund operators. This result followsfrom a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen's representation theorem of Calderón-Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates.