广义Fock空间上的Hankel算子

王晓峰, 夏锦, 陈建军

数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 561-572.

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PDF(494 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 561-572. DOI: 10.12386/A2019sxxb0053
论文

广义Fock空间上的Hankel算子

    王晓峰1, 夏锦1, 陈建军2
作者信息 +

Hankel Operators on Generalized Fock Spaces

    Xiao Feng WANG1, Jin XIA1, Jian Jun CHEN2
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文章历史 +

摘要

利用有界(消失)平均振荡函数的性质,本文刻画了一类广义Fock空间上的Hankel算子的有界性(紧性),同时,还刻画了换位子[MfP]的有界性和紧性,其中P是一个Toeplitz投影算子,而Mf表示符号为f的乘子.最后,应用Berezin变换来研究了BMO空间和VMO空间的几何性质.

Abstract

We characterize boundedness and compactness of Hankel operators on a very general class of weighted Fock spaces over Cn in terms of a certain notion of bounded and vanishing mean oscillation. The analogous description holds for the commutators[Mf, P] where Mf denotes the multiplication operator with symbol f and P is the Toeplitz projection. We also give geometric descriptions for the spaces BMO and VMO which are defined in terms of the Berezin transform.

关键词

广义Fock空间 / Hankel算子 / Berezin变换

Key words

Generalized Fock space / Hankel operator / Berezin transform

引用本文

导出引用
王晓峰, 夏锦, 陈建军. 广义Fock空间上的Hankel算子. 数学学报, 2019, 62(4): 561-572 https://doi.org/10.12386/A2019sxxb0053
Xiao Feng WANG, Jin XIA, Jian Jun CHEN. Hankel Operators on Generalized Fock Spaces. Acta Mathematica Sinica, Chinese Series, 2019, 62(4): 561-572 https://doi.org/10.12386/A2019sxxb0053

参考文献

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基金

国家自然科学基金资助项目(11471084;11301101);广东省青年创新人才项目(2017KQNCX220);肇庆学院校级课题项目(201732);肇庆学院博士启动项目(221622)

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