Onto Interpolation for the Dirichlet Space and for $H_1(\mathbb{D})$

Abstract

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 $H_1(\mathbb{D})$ 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 $H_1(\mathbb{D})$.

34 pages

References in corpus (2)

• Interpolating sequences in spaces with the complete Pick property
• Onto Interpolating Sequences for the Dirichlet Space

Cited by in corpus (2)

• Two-weight dyadic Hardy's inequalities
• A note on simply interpolating sequences for the Dirichlet space