Multiparameter Riesz commutators


It is shown that product BMO of S.-Y. A. Chang and R. Fefferman, defined on the space ${\Bbb R}^{d_1}\otimes \cdots \otimes {\Bbb R} ^{d_t}$, can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss, and at the same time extends the work of M. Lacey and S. Ferguson and M. Lacey and E. Terwilleger, on multiparameter commutators with Hilbert transforms.