A. P. Calderon-Zygmund and A. Zygmund did the ground-breaking works of singular integral in 1952. Studying the boundedness of singular integral operators in function spaces has become a very active and popular subject in harmonic Analysis. And many of the consolidation methods and techniques have been widely used in studying the boundedness of operators.As the commutators can be used to characterize the function spaces, com-mutators associated with singular integral operators are an important class of operator. Let T be the Calderon-Zygmund singular integral operator and b∈BMO(Rn), a classical result of Coifman, Rocherberg and Weiss states that the commutator [b,T](f)= bT(f)-T(bf) is bounded on Lp(Rn) for 1 |