Bergman 空间上的局部化与加权理论
Localization and weighted theory on the Bergman spaces
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中文总结 AI 辅助
本文在加权 Bergman 空间上引入弱局部化算子，用 Berezin 变换边界消失刻画其紧性，并给出双权 Toeplitz 算子紧性及 Bergman 投影有界性判据。
中文摘要 AI 辅助
本文研究了由双侧加倍权诱导的加权 Bergman 空间上的弱局部化算子类。我们首先建立了属于弱局部化算子范数闭包的算子的紧性特征，该特征以 Berezin 变换的边界消失性来刻画。我们的方法不同于文献中的方法，因为在我们的设置中，“平移”算子不能作为直接适用的工具。我们进一步刻画了双权设置下有界符号的 Toeplitz 算子的紧性，并给出了双权 Bergman 投影的有界性判据。
英文摘要
In this paper, we introduce the class of weakly localized operators on the weighted Bergman spaces induced by two-sided doubling weights. We first establish the characterization of the compactness of the operator belonging to the norm closure of weakly localized operators in terms of the boundary vanishing of the Berezin transform. Our approach here is different from the methods in the literature since the ``translation" operators are not served us a direct applicable tool in our setting. We further characterize the compactness of Toeplitz operators with bounded symbols in the two-weight setting, a boundedness criterion of a two-weight Bergman projection is also presented.
发表机构
- Jinan University（暨南大学）
- Northeast Normal University（东北师范大学）
- University of Eastern Finland（芬兰东芬兰大学）
- Chongqing University（重庆大学）
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