Bergman空间和q-Bloch空间之间的复合算子

Composition Operators Between Bergman Spaces and q-Bloch Spaces

本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子Cφ的有界性和紧性特征,得到了以下结论:(1)Cφ是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件; (2)Cφ是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件; (3)Cφ是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子 Cφ0的范数估计,此处Cφ0(f)(z)=foφ(z)-f(φ(0))．

This paper discusses the boundedness and compactness of composition operators Cφ between Bergman spaces and q-Bloch spaces as well as little q-Bloch spaces. It is obtained as follows： （1） the sufficient and necessary condition for Cφ0 to be bounded or compacted operators from B^q （or B0^q） to AP; （2） the sufficient and necessary condition for Cφ to be bounded or compacted operators from Ap to B^q; （3） the sufficient and necessary condition for Cφ to be bounded or compacted operators from Aα^p to B0^q. At the same time, the authors give some estimations for norm of the operator Cφ^0, where Cφ^0（f）（z） = f o φ（z） - f（φ（0））.