The compact composition operator on the μ-bergman space in the unit ball

Let p > 0 and μ be a normal function on [0,1), v(r)=(1-r2)1+npμ(r) for r ∈ [0,1). In this article, the bounded or compact weighted composition operator Tϕ,ψ from the μ-Bergman space Ap (μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator is compact from Ap(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that is compact on βμ for a > 1.