Onto interpolation for the Dirichlet space and for H1(D)

We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space H1(D) we define a natural notion of onto interpolation and we prove that the same condenser capacity condition characterizes all onto interpolating sequences. As a result, for sequences with finite associated measure, the problem of interpolation by an analytic function reduces to a problem of interpolation by a function in H1(D).