广义Bergman空间上的紧复合算子

张超

数学学报 ›› 2017, Vol. 60 ›› Issue (5) : 745-750.

PDF(352 KB)
PDF(352 KB)
数学学报 ›› 2017, Vol. 60 ›› Issue (5) : 745-750. DOI: 10.12386/A2017sxxb0063
论文

广义Bergman空间上的紧复合算子

    张超
作者信息 +

Compact Composition Operators on Generalized Bergman Spaces

    Chao ZHANG
Author information +
文章历史 +

摘要

首先证明广义Bergman空间AN,αp,(α>-n-1,p>0)上的复合算子Cφ的有界性和紧性是不依赖于p的,进而证明了若对某个 q> 0=和-n-1 < β < αCφAN,βp上有界,则CφAN,αp,(α>-n-1,p>0)上是紧的当且仅当lim|z|→1-((1-|z|2)/(1-|φz)|2))=0.

Abstract

We prove that the boundedness and compactness of the composition operators Cφ on generalized Bergman spaces AN,αp,(α>-n-1,p>0) are independent of p. On this foundation, we prove that if Cφ is bounded on AN,βp for some q> 0 and -n-1 < β < α, then Cφ is compact on AN,αp,(α>-n-1,p>0) if and only if lim|z|→1-((1-|z|2)/(1-|φ(z)|2))=0.

关键词

复合算子 / 广义Bergman空间 / 有界性 / 紧性

Key words

composition operator / generalized Bergman space / boundedness / compactness

引用本文

导出引用
张超. 广义Bergman空间上的紧复合算子. 数学学报, 2017, 60(5): 745-750 https://doi.org/10.12386/A2017sxxb0063
Chao ZHANG. Compact Composition Operators on Generalized Bergman Spaces. Acta Mathematica Sinica, Chinese Series, 2017, 60(5): 745-750 https://doi.org/10.12386/A2017sxxb0063

参考文献

[1] Cowen C. C., MacCluer B. D., Composition Operators on Spaces of Analytic Funtions, CRC Press, Boca Raton, 1995.
[2] Gu D. G., Weighted composition operators from generalized weighted Bergman spaces to weighted-type spaces, Inequal. and Appl., 2008, Article ID 619525, 14 pages.
[3] Rudin W., Function Theory in the Unit Ball of Cn, Springer-Verlag, New York, 1980.
[4] Tchoundja E., Carleson measures for the generalized Bergman spaces via a T (1)-type theorem, Ark. Mat., 2008, 46(2): 377-406.
[5] Zhang C., Cao G. F., Composition operators on generalized Bergman spaces, Adv. Math. China, 2014, 43(2): 295-300.
[6] Zhao R. H., Zhu K. H., Theory of Bergman spaces in the unit ball of Cn, Mém. Soc. Math. Fr. (N.S), 115, Paris, 2008.
[7] Zhu K. H., Compact composition operators on Bergman spaces of the unit ball, Houston J. Math., 2007, 33(1): 273-283.
[8] Zhu K. H., Operator Theory in Function Space, Marcel-Dekker, New York, 1990.
[9] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, Grad. Texts in Math., 226, Springer-Verlag, New York, 2004.
[10] Zhu X. L., Generalized composition operators from generalized weighted Bergman spaces to Bloch type spaces, Korean Math. Soc., 2014, 46(6): 1219-1232.

基金

国家自然科学基金资助项目(11501136);广东第二师范学院博士基金资助项目(2014ARF04)

PDF(352 KB)

Accesses

Citation

Detail

段落导航
相关文章

/