Multiplication operators on Sobolev disk algebra

摘要

In this paper, we study the algebra consisting of analytic functions in the Sobolev space W~(2,2)(D) (D is the unit disk), called the Sobolev disk algebra, explore the properties of the multiplication operators M_f on it and give the characterization of the corn-mutant algebra A'(M_f) of M_f. We show that A'(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.