On Multipliers of Dirichlet Type Spaces

Let M(D-K) be the class of multipliers of a Dirichlet type space D-K. Under conditions of the weight function K, we first characterize the interpolating sequences for M(D-K). Secondly, we study boundary values space D-K (partial derivative D) and its multiplier spaces M(D-K (partial derivative D)). We give a solution of partial derivative-equation in D-K (partial derivative D). In addition, by a derivative-free characterization of D-K spaces and standard techniques, we establish the partial derivative-equation and corona theorem for M(D-K). Corona type decomposition theorem on M(D-K) is also obtained.