  It is shown that product BMO of Chang and Fefferman, defined on the product
of Euclidean spaces can be characterized by the multiparameter commutators of
Riesz transforms. This extends a classical one-parameter result of Coifman,
Rochberg, and Weiss, and at the same time extends the work of Lacey and
Ferguson and Lacey and Terwilleger on multiparameter commutators with Hilbert
transforms. The method of proof requires the real-variable methods throughout,
which is new in the multi-parameter context.
