COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

Let Un be the unit polydisc of ℂn and φ=(φ1,*,φn) a holomorphic self-map of Un. This paper shows that the composition operator Cφ induced by φ is bounded on the little Bloch space β0*(Un) if and only if φl∈β0*(Un) for every l=1,2,*,n, and also gives a sufficient and necessary condition for the composition operator Cφ to be compact on the little Bloch space β0*(Un).