Composition Operators of Bloch-Type Spaces on Bounded Symmetric Domains

Let B-X be a bounded symmetric domain realized as the open unit ball B-X of a finite dimensional JB*-triple X. In this paper, we continue the work related to the composition operator C-phi between Bloch-type spaces, where phi is a holomorphic mapping from B-X into the unit polydisc U-n in C-n. We first give a necessary and sufficient condition for the composition operator from the alpha-Bloch space into the beta-Bloch space to be bounded. Next, we give a necessary condition for C-phi to be compact.

Automated summary

In this paper, we investigate the composition operator C-phi between Bloch-type spaces and provide necessary conditions for its boundedness and compactness.