摘要
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）.
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）.
基金
SupportedbytheNationalNaturalScienceFoundationofChina(10371091,10001030),andLiuHuiCenterforAppliedMathematics,NankaiUniversityandTianjinUniversity
