对布拉什克乘积子级集面积的精确估算

arXiv - MATH - Complex Variables Pub Date : 2024-07-28 DOI:arxiv-2407.19539

David Kalaj

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引用次数: 0

摘要

让 $\mathbb{D}$ 是复平面上的单位盘。在其他结果中，我们证明了有限布拉斯克乘积的如下奇特结果： $$B(z)=e^{is}\prod_{k=1}^d \frac{z-a_k}{1-z \overline{a_k}}。$$B 的子级集的 Lebesgue 度量在 $t \in[0,1]$ 时满足以下尖锐不等式：$$||{z\in \mathbb{D}:|B(z)|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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A sharp estimate of area for sublevel-set of Blaschke products

Let $\mathbb{D}$ be the unit disk in the complex plane. Among other results, we prove the following curious result for a finite Blaschke product: $$B(z)=e ^{is}\prod_{k=1}^d \frac{z-a_k}{1-z \overline{a_k}}.$$ The Lebesgue measure of the sublevel set of $B$ satisfies the following sharp inequality for $t \in [0,1]$: $$|\{z\in \mathbb{D}:|B(z)|

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arXiv - MATH - Complex Variables

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