Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain cri...Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.展开更多
In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factoriza...In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factorization theorems are obtained.展开更多
In this paper, the Nevanlinna class of holomorphlc functions on compact bordered Riemann surface Ω is discussed. This class is denoted by N(Ω), containing the class H^p(Ω). It is proved that f∈N(Ω) if and only if...In this paper, the Nevanlinna class of holomorphlc functions on compact bordered Riemann surface Ω is discussed. This class is denoted by N(Ω), containing the class H^p(Ω). It is proved that f∈N(Ω) if and only if f=φ/ψ,where φ and ψ are bounded holomorphic functions in Ω,and the Fatou boundary property is discussed.展开更多
文摘Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.
基金Supported by the National Natural Science Foundation of China (Grant No30800244)
文摘In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factorization theorems are obtained.
文摘In this paper, the Nevanlinna class of holomorphlc functions on compact bordered Riemann surface Ω is discussed. This class is denoted by N(Ω), containing the class H^p(Ω). It is proved that f∈N(Ω) if and only if f=φ/ψ,where φ and ψ are bounded holomorphic functions in Ω,and the Fatou boundary property is discussed.
