不同空间上的加权复合微分算子
发布时间：2018-08-15 13:37
【摘要】：加权复合微分算子是算子理论中的重要内容之一,反映了微分算子性质与其定义函数性质之间的关系,建立起算子理论与函数理论之间的关系.本文主要利用函数空间理论,研究在单位开圆盘Δ上从Bloch空间到加权型空间、Bers型空间上加权复合微分算子的性质.首先研究了单位开圆盘Δ上从Bloch空间到加权型空间上加权复合微分算子uDC_φ的有界性和紧性,得到了该算子有界的充分必要条件和紧的充分必要条件.然后考虑了单位开圆盘Δ上从Bers型空间上加权复合微分算子uDC_φ的有界性和紧性,得到了该算子有界的充分必要条件和紧的充分必要条件。
[Abstract]:Weighted Compound Differential Operator is one of the important contents of operator theory, which reflects the relationship between the property of differential operator and the property of its defined function, and establishes the relationship between operator theory and function theory.In this paper, we mainly use the theory of function space to study Bloch space to weighted space and Bers space on unit open disk_. The boundedness and compactness of the weighted composite differential operator uDC_phi on the unit open disk_from Bloch space to weighted type space are studied. The necessary and sufficient conditions for the operator to be bounded and compact are obtained. Then the weighted composite differential operator on the unit open disk_from Bers type space is considered. The necessary and sufficient conditions for the boundedness and compactness of the operator uDC_phi are obtained.
【学位授予单位】：贵州师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.3
本文编号：2184363
[Abstract]:Weighted Compound Differential Operator is one of the important contents of operator theory, which reflects the relationship between the property of differential operator and the property of its defined function, and establishes the relationship between operator theory and function theory.In this paper, we mainly use the theory of function space to study Bloch space to weighted space and Bers space on unit open disk_. The boundedness and compactness of the weighted composite differential operator uDC_phi on the unit open disk_from Bloch space to weighted type space are studied. The necessary and sufficient conditions for the operator to be bounded and compact are obtained. Then the weighted composite differential operator on the unit open disk_from Bers type space is considered. The necessary and sufficient conditions for the boundedness and compactness of the operator uDC_phi are obtained.
【学位授予单位】：贵州师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.3
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相关期刊论文 前5条
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，本文编号：2184363
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