Bloch空间上加权复合算子的紧性
The Compactness of Weighted Composition Operator on Bloch Sapce
DOI: 10.12677/PM.2018.81001, PDF,    科研立项经费支持
作者: 肖嘉琪, 马卓仕：嘉应学院，数学学院，广东 梅州
关键词: Bloch空间；加权复合算子；紧性；Bloch Space； Weighted Composition Operator； Compactness
摘要: 若f是单位圆盘D上的解析函数，定义加权复合算子如下： 借助Ψ 和φ 的函数特征给出了加权复合算子WΨ，φ 在Bloch空间上紧性的刻画。
Abstract: If f is an analytic function in the unit disk D , the weighted composition operator is defined as following: . In this paper, using the function theoretic of Ψ and φ characterize the compactness of weighted composition operator on Bloch space.
文章引用：肖嘉琪, 马卓仕. Bloch空间上加权复合算子的紧性[J]. 理论数学, 2018, 8(1): 1-7. https://doi.org/10.12677/PM.2018.81001

参考文献

[1] Axler, S. (1986) The Bergman space, the Bloch Space and Commutators of Multiplication Operators. Duke Mathematical Journal, 53, 315-332. [Google Scholar] [CrossRef] 
[2] Garnett, J. (1981) Bounded Analytic Functions. Academic Press, New York.
[3] Colonna, F. (2013) New Criteria for Boundedness and Compactness of Weighted Composition Operators Mapping into the Bloch Space. Central European Journal of Mathematics, 11, 55-73.
[4] Colonna, F. (2013) Weighted Composition Operators between and BMOA. Bulletin of the Korean Mathematical Society, 50.
[5] Galindo, P., Laitila, J., Lindsrom, M. (2013) Essential Norm Estimates for Composition Operators on BMOA. Journal of Functional Analysis, 265, 629-643. [Google Scholar] [CrossRef] 
[6] Bourdon, P., Cima, J. and Matheson, A. (1999) Compact Composition Operators on BMOA. Transactions of the American Mathematical Society, 351, 2183-2196. [Google Scholar] [CrossRef] 
[7] Hyyarinen, O. and Lindstrom, M. (2012) Estimates of Essential Norms of Weighted Composition Operators between Bloch-Type Spaces. Journal of Mathematical Analysis & Applications, 393, 38-44. [Google Scholar] [CrossRef] 
[8] Laitiala, J. (2009) Weighted Composition Operators on BMOA. Computational Methods & Function Theory, 9, 27-46.
[9] Laitiala, J. and Lindstrom, M. (2015) The Essential Norm of a Weighted Composition Operator on BMOA. Mathematische Zeitschrift, 279, 423-434. [Google Scholar] [CrossRef] 
[10] Liu, X. and Li, S. (2017) Norm and Essential Norm of a Weighted Composition Operator on the Bloch Space. Integral Equations & Operator Theory, 1-17.
[11] Smith, W. (1999) Compactness of Composition Operators on BMOA. Proceedings of the American Mathematical Society, 127, 2715-2725. [Google Scholar] [CrossRef] 
[12] Wulan, H. (2007) Compactness of Composition Operators on BMOA and VMOA. Science in China (Series A: Mathematics), 50, 997. [Google Scholar] [CrossRef] 
[13] Wulan, H., Zheng, D. and Zhu, K. (2009) Compact Composition Operators on BMOA and the Bloch Space. Proceedings of the American Mathematical Society, 137, 3861-3868. [Google Scholar] [CrossRef] 

为你推荐