Heisenberg群上与Schr?dinger算子有关的交换子的紧性
Compactness of Commutators Related with Schr?dinger Operators on Heisenberg Groups
DOI: 10.12677/PM.2022.125087, PDF,    科研立项经费支持
作者: 杨 丽, 代甜甜：青岛大学数学与统计学院，山东 青岛
关键词: 紧性；交换子；Heisenberg群；Schr?dinger算子；Compactness； Commutator； Heisenberg Group； Schr?dinger Operator
摘要: 让L表示一个Schrӧdinger算子。本文研究了Heisenberg群上与L有关的交换子的紧性问题。通过光滑截断技术，证明了Heisenberg群上分数Schrӧdinger热半群生成的积分算子关于消失平均震荡型空间CMO(ρ)(Hn)中函数的交换子是紧算子。作为应用，讨论了与L有关的极大函数交换子的紧性。
Abstract: Let L denote the Schrӧdinger operator. In this paper, we study the result of compactness of commutators related to L on Heisenberg groups. By smooth truncation technique, we show that commutators of the maximal operators generated by fractional Schrӧdinger heat semi groups with the function in the vanishing mean oscillation type space CMO(ρ)(Hn) are compact operators. As an application, we investigate compactness of commutators of maximal functions associated with L.
文章引用：杨丽, 代甜甜. Heisenberg群上与Schr?dinger算子有关的交换子的紧性[J]. 理论数学, 2022, 12(5): 764-775. https://doi.org/10.12677/PM.2022.125087

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