  We study boundedness properties of a class of multiparameter paraproducts on
the dual space of the dyadic Hardy space H_d^1(T^N), the dyadic product BMO
space BMO_d(T^N). For this, we introduce a notion of logarithmic mean
oscillation on the polydisc. We also obtain a result on the boundedness of
iterated commutators on BMO([0,1]^2).
