谐函数 $$alpha $$ 的尖锐点估计

IF 0.7 4区数学 Q2 MATHEMATICS

Complex Analysis and Operator Theory Pub Date : 2024-07-20 DOI:10.1007/s11785-024-01578-2

David Kalaj

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引用次数: 0

摘要

让（\alpha >-1\）并假定f是定义在单位盘上的$\alpha $-谐映射，它属于哈代类$h^p$，具有$p\geqslant 1$。我们得到了一些关于 $|f(z)|le g(|r|) \Vert f^*\Vert _p$ 和 $|Df(z)|le h(|r|)\Vert f^*\Vert _p$ 类型的尖锐估计。我们还证明了一类固定原点的单位盘到自身上的（\α \）-谐映射的 Schwarz 型 Lemma。

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Sharp Pointwise Estimate of $$\alpha $$ -Harmonic Functions

Let $\alpha >-1$ and assume that f is $\alpha $-harmonic mapping defined in the unit disk that belongs to the Hardy class $h^p$ with $p\geqslant 1$. We obtain some sharp estimates of the type $|f(z)|\le g(|r|) \Vert f^*\Vert _p$ and $|Df(z)|\le h(|r|)\Vert f^*\Vert _p$. We also prove a Schwarz type lemma for the class of $\alpha $-harmonic mappings of the unit disk onto itself fixing the origin.

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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.