Abstract: | Let CΓ be the Cauchy integral operator on a Lipschitz curve Γ. In this article, the authors show that the commutator b,CΓ] is bounded (resp, compact) on the Morrey space for any (or some) p ∈ (1,∞) and λ ∈ (0,1) if and only if (resp, ). As an application, a factorization of the classical Hardy space in terms of CΓ and its adjoint operator is obtained. |