Multipoint Julia theorems

IF 0.6 4区 数学 Q3 MATHEMATICS
M. Abate
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引用次数: 0

Abstract

Following ideas introduced by Beardon-Minda and by BaribeauRivard-Wegert in the context of the Schwarz-Pick lemma, we use the iterated hyperbolic difference quotients to prove a multipoint Julia lemma. As applications, we give a sharp estimate from below of the angular derivative at a boundary point, generalizing results due to Osserman, Mercer and others; and we prove a generalization to multiple fixed points of an interesting estimate due to Cowen and Pommerenke. These applications show that iterated hyperbolic difference quotients and multipoint Julia lemmas can be useful tools for exploring in a systematic way the influence of higher order derivatives on the boundary behaviour of holomorphic self-maps of the unit disk.
多点Julia定理
根据Beardon-Minda和baribeauriward - wegert在Schwarz-Pick引理中引入的思想,我们使用迭代双曲差商来证明一个多点Julia引理。作为应用,我们给出了边界点处角导数的从下估计,推广了Osserman, Mercer等人的结果;并且我们证明了Cowen和Pommerenke的一个有趣估计的多不动点的推广。这些应用表明,迭代双曲差商和多点Julia引理可以系统地探索高阶导数对单位盘全纯自映射边界行为的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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