Composition Cesàro Operator on the Normal Weight Zygmund Space in High Dimensions

Let n > 1 and B be the unit ball in n dimensions complex space C n . Suppose that φ is a holomorphic self-map of B and ψ ∈ H ( B ) with ψ (0) = 0. A kind of integral operator, composition Cesàro operator, is defined by T φ ψ ( f ) ( z ) = ∫ 0 1 f [ φ ( t z ) ] R ψ ( t z ) d t t f ∈ H ( B ) z ∈ B . In this paper, the authors characterize the conditions that the composition Cesàro operator T φ,ψ is bounded or compact on the normal weight Zygmund space Z μ ( B ) . At the same time, the sufficient and necessary conditions for all cases are given.