Dyadic BMO on the bidisk.
We give several new characterizations of the dual of the dyadic Hardy space H(T), the so-called dyadic BMO space in two variables and denoted BMO . These include characterizations in terms of Haar multipliers, in terms of the "symmetrised paraproduct" Λ, in terms of the rectangular BMO norms of the iterated "sweeps", and in terms of nested commutators with dyadic martingale transforms. We further explore the connection between BMO and John-Nirenberg type inequalities,...