以拟齐次函数为符号的H-Toeplitz算子与JH-Toeplitz算子
H-Toeplitz Operator and JH-Toeplitz Operator with Quasi Homogeneous Functions as Symbols
DOI: 10.12677/pm.2025.156190, PDF,    国家自然科学基金支持
作者: 曹璎元*, 董 玉：辽宁师范大学数学学院，辽宁 大连
关键词: 调和Bergman空间；H-Toeplitz算子；JH-Toeplitz算子；交换性；Harmonic Bergman space； H-Toeplitz Operator； JH-Toeplitz Operator； Interchangeability； Quasi Commutativity
摘要: 本文研究了调和Bergman空间中的H-Toeplitz算子，并定义了调和Bergman空间上的JH-Toeplitz算子，给出了两个以拟齐次函数为符号的H-Toeplitz算子的交换性的充要条件。本文还讨论了以拟齐次函数为符号的H-Toeplitz算子与JH-Toeplitz算子乘积的相关理论。
Abstract: This article studies the H-Toeplitz operator in harmonic Bergman space and defines the JH-Toeplitz operator on harmonic Bergman space. The necessary and sufficient conditions for the commutativity of two H-Toeplitz operators with quasi homogeneous functions as symbols are given. The article also discusses the relevant theories of the product of H-Toeplitz operator and JH-Toeplitz operator with quasi homogeneous functions as symbols.
文章引用：曹璎元, 董玉. 以拟齐次函数为符号的H-Toeplitz算子与JH-Toeplitz算子[J]. 理论数学, 2025, 15(6): 69-77. https://doi.org/10.12677/pm.2025.156190

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