Multiplication operators on Sobolev disk algebra

摘要

In this paper, we study the algebra consisting of analytic functions in the Sobolev space W2,2(D) (D is the unit disk), called the Sobolev disk algebra, explore the properties of the multiplication operators Mf on it and give the characterization of the commutant algebra A'(Mf) of Mf. We show that A'(Mf) is commutative if and only if Mf* is a Cowen-Douglas operator of index 1.