Carleson embeddings

Abstract

In this paper we discuss several operator ideal properties for so called Carleson embeddings of tent spaces into specific $L^q\left(\mu \right)$-spaces, where $\mu$ is a Carleson measure on the complex unit disc. Characterizing absolutely $q$-summing, absolutely continuous and $q$-integral Carleson embeddings in terms of the underlying measure is our main topic. The presented results extend and integrate results especially known for composition operators on Hardy spaces as well as embedding theorems for function spaces of similar kind.