多圆柱上Bloch型空间之间复合算子紧性条件的有关讨论

A discussion on compactness conditions of composition operator between Bloch-type spaces in the polydisc

设U^n是n维复空间C^n中的单位多圆柱,φ=(φ_1,…,φ_n)是U^n到自身的一个全纯映射,文中探讨了Bloch型空间β~p(U^n)(p>0)上复合算子C_φ几个紧性条件是否具有等价性,并给出了紧性条件的最简表示.

Let Un be the unit polydisc in C^n, and φ=（φ1,…φn）a holomorphic self-mapping on U^n. In this paper, several equivalent representations for composition operator Cφ to be compact on Bloch-type spaces β^p（U^n）（p〉0） are discussed, and the simplest representations of compact conditions are given.