Growth spaces on circular domains taking values in a banach lattice, embeddings and composition operators

Official URL: https://dx.doi.org/10.3390/math12162554

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.