Composition type operator from Bergman space to μ-Bloch type space in Cn ✩

Let ϕ be a holomorphic self-map of B and ψ ∈ H(B). A composition type operator Tψ,ϕ is defined by Tψ,ϕ(f ) = ψf ◦ ϕ. We can regard this operator as a generalization of a multiplication operator and a composition operator. For normal functions μ, some necessary and sufficient conditions are given for which Tψ,ϕ is a bounded or compact operator from Bergman space to μ-Bloch type space βμ on the unit ball of Cn. As a Corollary, we obtain the pointwise multiplier from Bergman space to μ-Bloch type space on B.  2004 Elsevier Inc. All rights reserved