Bloch型空间到Zygmund型空间的广义Cesàro算子和复合算子的积

Products of Extended Cesàro Operator and Composition Operator from Bloch-type Spaces to Zygmund-type Spaces

ω和μ是[0,1)上的正规函数,g是单位球Bn上的全纯函数,φ是Bn上的全纯自映射,由g和φ诱导的算子TgCφ∶Bω(Bω,0)→Zμ(Zμ,0)定义为:TgCφf(z)=∫0 1 f(φ(tz))Rg(tz)dt/t,z∈Bn,f∈Bω(Bω,0).给出了该算子从Bloch型空间到Zygmund型空间有界和紧的充要条件.

Let ω and μ be normal function,g be holomorphic function on the unit ball and φ be holomorphic self-mapping of Bn.The operator TgCφ∶Bω（Bω,0）→Zμ（Zμ,0） induced by gand ,defined by TgCφ f（z）=∫0 1 （fφ）（tz）Rg（tz）dt/t,z∈Bn,f∈ Bω（Bω,0）.This paper gives some necessary and sufficient conditions for the operator TgCφ from Bloch-type spaces to Zygmund-type spaces.