We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón--Zygmund operators. This result follows from 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.
"Upper Bound for Multi-Parameter Iterated Commutators." Publ. Mat. 60 (1) 191 - 220, 2016.