On Carleson Embeddings Of Star-invariant Supspaces

Abstract

Embeddings of star-invariant subspaces K ^p _θ of H ^p determined by an inner function θ are studied. Using a method of Aleksandrov, it is shown that the embedding into L ^p (μ) is compact whenever μ satisfies a certain vanishing condition with respect to the singular set of θ. Conversely, if the embedding is compact, and θ is a so-called one-component inner function, the measure is shown to satisfy a different vanishing condition.

Keywords:

• BACKWARD SHIFT
• STAR-INVARIANT SUBSPACE
• CARLESON MEASURE