ITERATED COMMUTATORS UNDER A JOINT CONDITION ON THE TUPLE OF MULTIPLYING FUNCTIONS

We present a pair of joint conditions on the two functions b(1), b(2) strictly weaker than b(1), b(2) is an element of BMO that almost characterize the L-2 bounded-ness of the iterated commutator [b(2), [b(1), T]] of these functions and a Calderon-Zygmund operator T. Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.Peer reviewe