Logarithmic Mean Oscillation on the Polydisc, Multi-Parameter Paraproducts and Iterated Commutators

Abstract

Abstract. We introduce another notion of bounded logarithmic mean oscillation in the N -torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO, bmo d (T N ) to the dyadic product BMO space, BMO d (T N ). We also obtain a sufficient condition for the boundedness of the iterated commutators from the subspace of bmo(R N ) consisting of functions with support in [0,1] N to BMO(R N ).