INTERPOLATING SEQUENCES FOR THE DIRICHLET SPACE AND ITS MULTIPLIERS

We characterize the universal interpolating sequences for the Dirichlet space, D, and reduce the characterization of the usual interpolating sequences to a question about zero sets for D. We answer some questions of Axler by giving sufficient conditions for a sequence to be interpolating for M(D), the multipliers of D, and characterize the interpolating sequences for D and M(D) which lie on a radius. For example, we show {1 − exp(−a n )} is interpolating for any a > 1 and that this is essentially best possible. We also give some sufficient conditions for interpolation inD ∩ H 1 and M(D�), 0 < � < 1/2.

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