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