指数权Bergman空间Aφp和Aφ∞间的算子

何忠华, 王晓峰, 刘柚岐

数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 655-668.

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数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 655-668. DOI: 10.12386/A2021sxxb0056
论文

指数权Bergman空间Aφp和Aφ∞间的算子

    何忠华1, 王晓峰2, 刘柚岐2
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Toeplitz Operators Between Bergman Spaces with Exponential Weights Aφp and Aφ∞

    Zhong Hua HE1, Xiao Feng WANG2, You Qi LIU2
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摘要

本文主要讨论单位圆盘上指数权Bergman空间Aφp和Aφ∞（0 < p < ∞）之间由正Borel测度μ所诱导的Toeplitz算子Tμ，借助Berezin变换和平均函数刻画该类算子的有界性和紧性.

Abstract

We consider Toeplitz operators Tμ with positive Borel measure symbol μ between Bergman spaces Aφp and Aφ∞ for 0 < p < ∞, where Aφp is Bergman space on the unit disk D with exponential weights. Some characterizations of their boundedness and compactness are given in terms of Berezin transforms and averaging functions.

关键词

指数权Bergman空间 / Toeplitz算子 / Berezin变换 / 平均函数

Key words

Bergman space with exponential weights / Toeplitz operators / Berezin transform / averaging function

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何忠华, 王晓峰, 刘柚岐. 指数权Bergman空间Aφp和Aφ∞间的算子. 数学学报, 2021, 64(4): 655-668 https://doi.org/10.12386/A2021sxxb0056
Zhong Hua HE, Xiao Feng WANG, You Qi LIU. Toeplitz Operators Between Bergman Spaces with Exponential Weights Aφp and Aφ∞. Acta Mathematica Sinica, Chinese Series, 2021, 64(4): 655-668 https://doi.org/10.12386/A2021sxxb0056

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基金

国家自然科学基金（11971125，11971123）；广东省高校重点科研平台与科研项目（2018KZDXM048）
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