Bloch functions on bounded symmetric domains

We introduce and characterize Bloch functions on bounded symmetric domains, which may be infinite dimensional, by extending several well-known equivalent conditions for Bloch functions on the open unit disc U in C. We also generalize a number of results concerning Bloch functions on U to bounded symmetric domains. Given a holomorphic mapping phi between bounded symmetric domains Beta x and Beta y, we derive criteria for boundedness and compactness of the composition operator C-phi between the Bloch spaces beta(Beta(Upsilon)) and beta(Beta(Chi)), extending several known results for finite dimensional domains. (C) 2016 Elsevier Inc. All rights reserved.