Georgia Institute of Technology College of Sciences

In this work we prove that the space of two parameter, matrix-valued BMO functions can be characterized by considering iterated commutators with the Hilbert transform. Specifically, we prove that the norm in the BMO space is equivalent to the norm of the commutator of the BMO function with the Hilbert transform, as an operator on L^2. The upper bound estimate relies on a representation of the Hilbert transform as an average of dyadic shifts, and the boundedness of certain paraproduct operators, while the lower bound follows Ferguson and Lacey's wavelet proof for the scalar case.