Reducibility for a Class of Analytic Multipliers on the Dirichlet Space

摘要

It is proved that if phi is a finite Blaschke product with four zeros, then M-phi is reducible on the Dirichlet space with norm parallel to parallel to if and only if phi = phi(1) omicron phi(2), where phi(1), phi(2) are Blaschke products and phi(2) is equivalent to z(2). Also, the same reducibility of M-phi with finite Blaschke product phi on the Dirichlet space under the equivalent norms parallel to parallel to(1) and parallel to parallel to(0) is given.