加权Bergman空间上的广义Volterra型积分算子
Generalized Volterra Type Integral Operators between Weighted Bergman Spaces
DOI: 10.12677/PM.2022.1212229, PDF, HTML, 下载: 166  浏览: 302  科研立项经费支持
作者: 施业成：岭南师范学院，广东 湛江
关键词: Bergman 空间；广义 Volterra 型积分算子；有界性；紧性；Bergman Spaces； Generalized Volterra Type Integral Operators； Boundedness； Compactness
摘要: 近年来解析函数空间上的广义 Volterra 型积分算子的有界性和紧性引起众多学者的兴趣。然而，加权 Bergman 空间上的广义 Volterra 型算子的研究尚未完善。本论文讨论加权Bergman空间之间的广义 Volterra 型积分算子的有界性和紧性问题，利用 Bergman Carleson 测度和Littlewood-Paley 公式给出了加权 Bergman 空间之间的广义 Volterra 型积分算子的有界性和紧性的刻画，完善了加权 Bergman 空间上的广义 Volterra 型算子的性质。
Abstract: In recent years, the boundedness and compactness of generalized Volterra-type integral operators on analytic function spaces have attracted many scholars' interests, but the study of the generalized Volterra-type integral operators on weighted Bergman space is not yet complete. In this paper, we consider the boundedness and compactness of Generalized Volterra type integral operators between weighted Bergman spaces. Using the Bergman Carleson measure and Littlewood-Paley formula, we characterized the boundedness and compactness of generalized Volterra-type operators weighted Bergman space, and the properties of generalized Volterra-type operators were further improved.
文章引用：施业成. 加权Bergman空间上的广义Volterra型积分算子[J]. 理论数学, 2022, 12(12): 2133-2140. https://doi.org/10.12677/PM.2022.1212229

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