利普希茨空间到有界解析函数空间的加权微分复合算子Weighted Differentiation Composition Operators from Lipschitz Space to Bounded Analytic Function Space
张亮
摘要(Abstract)：
加权微分复合算子理论是算子领域的重要组成部分.不同空间的加权微分复合算子的有界性和紧致性被深入地研究并出现了许多成果.在此基础上给出了单位圆盘上从利普希茨空间到有界解析函数空间的加权微分复合算子有界和紧致的性质,并证明了算子有界和紧致的充要条件.
关键词(KeyWords)： 利普希茨空间;有界解析函数空间;加权微分复合算子
基金项目(Foundation): 国家自然科学基金资助项目(10971153),国家自然科学基金资助项目(10671141)
作者(Author): 张亮
DOI: 10.16393/j.cnki.37-1436/z.2011.05.003
参考文献(References)：
- [1]Stevi'c S.Norm of weighted composition operators from Bloch space to on the unit ball[J].Ars Combinatoria,2008,88:125–127.
- [2]Stevi'c S.On a new operator fromto the Bloch-type space on the unit ball[J].Utilitas Mathematica,2008,77:257-263.
- [3]Wulan H,Zhou J.Type spaces of analytic functions[J].Journal of Function Spaces and Applications,2006,4(1):73-84.
- [4]Zhou Z H,Shi J H.Compactness of composition operators on the Bloch space in classical bounded symmetric domains[J].MichiganMath,2002,50:381-405.
- [5]Hu Z,Wang S.Composition operators on Bloch-type spaces[J].Proceedings of the Royal Society of EdinburghA,2005,135(6):1229-1239.
- [6]Cowen C C,MacCluer B D.Composition operators on spaces of analytic functions[M].CRC Press,Boca Raton,FL,1995.
- [7]Zhu K H.Spaces of holomorphic functions in the unit ball[M].New York:Springer,2005.