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Pure Mathematics 2025
以拟齐次函数为符号的H-Toeplitz算子与JH-Toeplitz算子
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Abstract:
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。
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.
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