Let U^n be the unit polydisc of C^n and φ（φ,…,φ） a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0＊（U^n） if and only if φ ...Let U^n be the unit polydisc of C^n and φ（φ,…,φ） a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0＊（U^n） if and only if φ ∈β0＊（U^n） for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0＊ （U^n）.展开更多
In this note, we consider power series f w(z)=∑∞n=0a ne iw n z nwhere moduli a n of the coefficients are given but the argument α n are random. We discuss the conditions of f w is in α_ Bloch space ...In this note, we consider power series f w(z)=∑∞n=0a ne iw n z nwhere moduli a n of the coefficients are given but the argument α n are random. We discuss the conditions of f w is in α_ Bloch space and little α_ Bloch space. Our results generalize Anderson, Clunie and Pommerenke's.展开更多
文摘Let U^n be the unit polydisc of C^n and φ（φ,…,φ） a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0＊（U^n） if and only if φ ∈β0＊（U^n） for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0＊ （U^n）.
文摘In this note, we consider power series f w(z)=∑∞n=0a ne iw n z nwhere moduli a n of the coefficients are given but the argument α n are random. We discuss the conditions of f w is in α_ Bloch space and little α_ Bloch space. Our results generalize Anderson, Clunie and Pommerenke's.
