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

• 作者: Si XU Xuejun ZHANG Shenlian LI
• 来源期刊: 数学年刊B辑（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 69-84
• 页数: 16页
• 语种: 英文
• DOI: 10.1007/s11401-021-0245-x

摘要

Let n＞1 and B be the unit ball in n dimensions complex space Cn.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 Tφ,ψ(f)(z)= ∫10f[φ(tz)]Rψ(tz)dt/t,f ∈ H(B),z ∈ B.In this paper,the authors characterize the conditions that the composition Cesàro operatorTφ,ψis bounded or compact on the normal weight Zygmund space Zμ(B).At the same time,the sufficient and necessary conditions for all cases are given.