Compact Composition Operator of Two Sequences Symbols on μ-Bergman Space in the Unit Ball

Abstract

Let ϵ≥0 and μ be a normal function on [0,1),ν(1-ϵ)=(2ϵ-ϵ^2 )^2 μ(1-ϵ) for ϵ<1. The bounded or compact weighted composition operator of two sequences symbols T_(φ_r,ψ_r ) from the μ-Bergman space A^(1+ϵ) (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 of sequence symbols C_(φ_r ) is compact from A^(1+ϵ) (μ) to β_ν is given. The briefly sufficient and necessary condition that C_(φ_r ) is compact on β_μ for ϵ>0 is given.