具有 C⌃2 边界的域 D 边界中代数 A(D) 的豪斯多夫维度为 2n - 1 的峰集

IF 0.7 4区数学 Q2 MATHEMATICS

Complex Analysis and Operator Theory Pub Date : 2024-05-02 DOI:10.1007/s11785-024-01532-2

Piotr Kot

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引用次数: 0

摘要

我们考虑一个边界为（C^{2}\）的有界严格伪凸域（（Omega \子集）mathbb {C}^{n}\）。然后，我们证明在 Hausdorff 维度为（0,2n-1]\）的 \(\partial \Omega \)的任何紧凑的 Ahlfors-David 正则子集包含一个 Hausdorff 维度等于 \(\beta \)的峰集 E。

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A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary

We consider a bounded strictly pseudoconvex domain \(\Omega \subset \mathbb {C}^{n}\) with \(C^{2}\) boundary. Then, we show that any compact Ahlfors–David regular subset of \(\partial \Omega \) of Hausdorff dimension \(\beta \in (0,2n-1]\) contains a peak set E of Hausdorff dimension equal to \(\beta \).

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来源期刊

Complex Analysis and Operator Theory 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

107

审稿时长

3 months

期刊介绍： Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.