Embedding Theorems for Dirichlet Type Spaces

Abstract

We use the Carleson measure-embedding theorem for weighted Bergman spaces to characterize the positive Borel measures $\unicode[STIX]{x1D707}$ on the unit disc such that certain analytic function spaces of Dirichlet type are embedded (compactly embedded) in certain tent spaces associated with a measure  $\unicode[STIX]{x1D707}$ . We apply these results to study Volterra operators and multipliers acting on the mentioned spaces of Dirichlet type.