  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 of Cotlar-Sadosky to
the product BMO of Chang-Fefferman. We also obtain a sufficient condition for
the boundedness of iterated commutators with Hilbert transforms betweeen the
strong notions of these two spaces.
