单位球上Zygmund空间到α-Bloch空间的复合算子

Composition Operators from Zygmund Spaces to α-Bloch Spaces in the Unit Ball

讨论了单位球上Zygmund空间Z到α-Bloch空间Bα的复合算子Cφ的有界性和紧性,得到了算子Cφ:Z→Bα为有界和紧的几个充要条件.给出了当μ(t)=(log e/(1-t2)-1时,μ-Bloch空间Bμ到α-Bloch空间Bα的复合算子Cφ为有界算子和紧算子的充要条件.

The boundedness and compactness of composition operators Cφ from the Zygmund space Z to the α-Bloch space Bα are discussed in the unit ball,and some sufficient and necessary conditions are obtained for the operator Cφ：Z→Bα to be bounded and compact. At the same time,the sufficient and necessary conditions are given for the composition operator Cφ to be bounded and compact from the μ-Bloch space Bα to the α-Bloch space Bα when μ（t）=（log e/（1-t2））-1.