COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

Abstract Let U n be the unit polydisc of ℂ n and φ = ( φ 1 , * , φ n ) a holomorphic self-map of U n . This paper shows that the composition operator C φ induced by φ is bounded on the little Bloch space β 0 * ( U n ) if and only if φ l ∈ β 0 * ( U n ) for every l = 1 , 2 , * , n , and also gives a sufficient and necessary condition for the composition operator C φ to be compact on the little Bloch space β 0 * ( U n ) .