调和Bergman空间上以${\left|z\right|}^2+a{z}^m+b{\bar{z}}^n$为符号的Toeplitz算子的正规性
Normality of Toeplitz Operator with ${\left|z\right|}^{}$

DOI: 10.12677/pm.2026.161015, PP. 122-126

郝蕾, 孙涛

Keywords: 调和Bergman空间，Toeplitz算子，算子正规性
Harmonic Bergman Space, Toeplitz Operator, Operator Normality

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Abstract:

本文刻画了在调和Bergman空间上以${\left|z\right|}^2+a{z}^m+b{\bar{z}}^n$ 为符号的Toeplitz算子的正规性问题。本文先对调和Bergman空间及Toeplitz算子的相关知识进行了介绍，梳理了调和Bergman空间、Toeplitz算子研究的具有代表性的相关成果。本文还给出了参数相关的以${\left|z\right|}^2+a{z}^m+b{\bar{z}}^n$ 为符号的Toeplitz算子在调和Bergman空间上的正规性的充分必要条件，在该充要条件的基础上提出了两个推论，建立及推广了该符号下Toeplitz算子的自伴性与正规性的等价关系，补充了这类算子结构性质的相关结论。
This paper investigates the normality of Toeplitz operators with the symbol

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