Composition type operators from Hardy spaces to μ-Bloch spaces on the unit ball

Let φ be a holomorphic self-map of Bn and ψ ∈ H( Bn). A composition type operator is defined by Tψ,φ(f)= ψf o φ for f ∈ H( Bn), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space Hp( Bn) to μ-Bloch space Bμ( Bn). The conditions are some supremums concerned with ψ, φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.