Bergman型空间到Bers型空间之加权复合算子

江治杰

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 67-74.

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 67-74. DOI: 10.12386/A2010sxxb0010
论文

Bergman型空间到Bers型空间之加权复合算子

    江治杰
作者信息 +

Weighted Composition Operator from Bergman-Type Spaces into Bers-Type Spaces

    Zhi Jie JIANG
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摘要

讨论了Bergman 型空间H(p,μ) 到Bers型空间Hβ、小Bers 型空间Hβ,0上的加权复合算子,给出了加权复合算子有界性、紧性、弱紧性的充要条件,以及紧复合算子的角导数准则. 本文还讨论了具有闭值域的加权复合算子,得到了一个充分条件.

 

Abstract

This paper investigates weighted composition operator from Bergman-type space into Bers-type space, and some necessnary and sufficient conditions of weighted composition operator to be bounded and compact and weak compact are obtained. The paper also gives the angular derivative rule of compactness of weighted composition operators. The paper also talks about weighted composition operator with closed range and a sufficient condition is given.

 

关键词

Bergman 型空间 / Bers型空间 / 加权复合算子

Key words

Bergman-type space / Bers-type space / weighted composition operator

引用本文

导出引用
江治杰. Bergman型空间到Bers型空间之加权复合算子. 数学学报, 2010, 53(1): 67-74 https://doi.org/10.12386/A2010sxxb0010
Zhi Jie JIANG. Weighted Composition Operator from Bergman-Type Spaces into Bers-Type Spaces. Acta Mathematica Sinica, Chinese Series, 2010, 53(1): 67-74 https://doi.org/10.12386/A2010sxxb0010

参考文献


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[4] Ohno S., Weighted composition operators between H and the Bloch space, Taiwan J. Math. Soc., 2001, 5(3): 555--563.

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[6] Choa J. S., Ohno S., Product of composition and Toeplitz operators, J. Math. Anal. Appl., 2003, 281: 320--331.

[7] Li S. X., Stev? S., Weighted composition operators from Bergman-type spaces into Bloch spaces, Proc. Indian Acad. Sci. (Math. Sci.), 2007, 117(3): 371--385.

[8] Hans J., Special operators on classical spaces of analytic function, Extracta Mathematicae, 2004, 19(1): 21--53.

基金

四川省教育厅重点基金资助项目(0720A04)

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