We characterize the boundedness and compactness of the product of extended Cesaro operator and composition operator TgCφ from generalized Besov spaces to Zygmund spaces, where g is a given holomorphic function in the...We characterize the boundedness and compactness of the product of extended Cesaro operator and composition operator TgCφ from generalized Besov spaces to Zygmund spaces, where g is a given holomorphic function in the unit disk D, φ is an analytic self-map of Ii） and TgC~ is defined byTgCφf（z）=∫z 0 f（φ（t））g′（t）dt.展开更多
Let n>1 and B be the unit ball in n dimensions complex space C^(n).Suppose thatφis a holomorphic self-map of B andψ∈H(B)withψ(0)=0.A kind of integral operator,composition Cesàro operator,is defined by T_(...Let n>1 and B be the unit ball in n dimensions complex space C^(n).Suppose thatφis a holomorphic self-map of B andψ∈H(B)withψ(0)=0.A kind of integral operator,composition Cesàro operator,is defined by T_(φ)ψ(f)(z)=∫^(1)0f[φ(tz)]Rψ(tz)dt/t,f∈(B)z∈B.In this paper,the authors characterize the conditions that the composition Cesàro operator T_φ,ψis bounded or compact on the normal weight Zygmund space Z_μ(B).At the same time,the sufficient and necessary conditions for all cases are given.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10771064） Supported by the Natural Science Foundation of Zhejiang Province（YT080197, Y6090036, Y6100219） Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province（T200924） Acknowledgement The author would like to express his thanks to his supervisor, Prof HU Zhang-jian, for his guidence.
文摘We characterize the boundedness and compactness of the product of extended Cesaro operator and composition operator TgCφ from generalized Besov spaces to Zygmund spaces, where g is a given holomorphic function in the unit disk D, φ is an analytic self-map of Ii） and TgC~ is defined byTgCφf（z）=∫z 0 f（φ（t））g′（t）dt.
基金supported by the National Natural Science Foundation of China(No.11571104)the Hunan Provincial Innovation Foundation for Postgraduate(No.CX2018B286)。
文摘Let n>1 and B be the unit ball in n dimensions complex space C^(n).Suppose thatφis a holomorphic self-map of B andψ∈H(B)withψ(0)=0.A kind of integral operator,composition Cesàro operator,is defined by T_(φ)ψ(f)(z)=∫^(1)0f[φ(tz)]Rψ(tz)dt/t,f∈(B)z∈B.In this paper,the authors characterize the conditions that the composition Cesàro operator T_φ,ψis bounded or compact on the normal weight Zygmund space Z_μ(B).At the same time,the sufficient and necessary conditions for all cases are given.
