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We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space   ( ), the dyadic product BMO space BMO ( ). 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]).

Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO