  We show that the product BMO space can be characterized by iterated
commutators of a large class of Calder\'on-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 Hyt\"onen's representation theorem of
Calder\'on-Zygmund operators as averages of dyadic shifts. The proof introduces
some new paraproducts which have BMO estimates.
