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 boundedon the little Bloch space β0?(Un) if and only if φl ∈ β0?(Un) for every l = 1, 2, · · · , n,and also gives a su?cient and necessary condition for the composition operator Cφ to becompact on the little Bloch space β0?(Un).