THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on 0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ 0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.

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), $v(r)={(1-r^2)}^{1+\frac{n}{p}\mu }\left(r\right)$ for r ∈ 0,1). In this article, the bounded or compact weighted composition operator T_?,ψ from the μ-Bergman space A^p (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 A^p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that is compact on β_μ for a > 1.