Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces

Let C-Gamma be the Cauchy integral operator on a Lipschitz curve Gamma. In this article, the authors show that the commutator [b,C-Gamma] is bounded (resp, compact) on the Morrey space Lp,lambda(R) for any (or some) p is an element of (1,infinity) and lambda is an element of (0,1) if and only if b is an element of BMO(R) (resp, CMO(R)). As an application, a factorization of the classical Hardy space H1(R) in terms of C-Gamma and its adjoint operator is obtained.