Growth Spaces on Circular Domains Taking Values in a Banach Lattice, Embeddings and Composition Operators

Abstract

We introduce the space of holomorphic growth spaces with values in a Banach lattice. We provide norm and essential norm estimates of the embedding operator, and we completely characterize the bounded and compact embeddings of the growth spaces using vector-valued Carleson measures. As an application, we prove a characterization of weighted composition operators.

Keywords

• embeddings
• composition operators
• growth spaces
• Banach lattice