单位球上Zygmund空间到α-Bloch空间的复合算子

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 戴济能 DAI Jineng1 1 2 3 first-author 欧阳才衡 OUYANG Caiheng1 1 中国科学院武汉物理与数学研究所 中国科学院武汉物理与数学研究所 Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences 武汉工程大学理学院 武汉工程大学理学院 School of Science,Wuhan Institute of Technology School of Science,Wuhan Institute of Technology 中国科学院研究生院 中国科学院研究生院 Graduate School of Chinese Academy of Sciences Graduate School of Chinese Academy of Sciences 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. 复合算子 Zygmund空间 Bloch空间 composition operator Zygmund space Bloch space 10.14188/j.1671-8836.2010.04.001 O177 国家自然科学基金资助项目（10571044） 2010-04-01 2021-04-01 4 56