弱一致完美域上的Bergman函数

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-03 DOI:10.1112/jlms.70107

Yuanpu Xiong, Zhiyuan Zheng

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引用次数: 0

摘要

我们构造了两类zalcman型域，在这两类域上Bergman距离函数表现出某些预先描述的边界行为。这样的例子也导致了统一完美性在Pommerenke意义上的一般化。这些弱一致完美条件可以用对数容量来表示。我们得到了在这些区域上Bergman核函数边界行为的较低估计。

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Bergman functions on weakly uniformly perfect domains

We construct two classes of Zalcman-type domains, on which the Bergman distance functions exhibit certain pre-described boundary behaviors. Such examples also lead to generalizations of uniform perfectness in the sense of Pommerenke. These weakly uniformly perfect conditions can be characterized in terms of the logarithm capacity. We obtain lower estimates for the boundary behaviors of Bergman kernel functions on such domains.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.