【摘 要】
：
Let Un be the unit polydisc of Cn and φ= (φ1,...,φn) a holomorphic self-map of Un. Let0 ≤α＜ 1. This paper shows that the composition operator Cφ is bounded
【机 构】
：
Department of Mathematics, LiuHui Center for Applied Mathematics
【基金项目】
：
国家自然科学基金;南开大学-天津大学合作项目
论文部分内容阅读
Let Un be the unit polydisc of Cn and φ= (φ1,...,φn) a holomorphic self-map of Un. Let0 ≤α＜ 1. This paper shows that the composition operator Cφ is bounded on the Lipschitz space Lipα(Un)if and only if there exists M ＞ 0 such that∑nk,l=1|φl/zk(z)|( 1-|zk|2/1-|φl(z)|2)1-α≤ Mfor z ∈ Un. Moreover Cφ is compact on Lipα(Un) if and only if Cφ is bounded on Lipα(Un) and for everyε＞ 0, there exists a δ＞ 0 such that∑nk,l=1|φl/zk(z)|( 1-|zk|2/1-|φl(z)|2)1-α≤εwhenever dist(φ(z), Un) ＜δ.
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