On L 1-estimates of derivatives of univalent rational functions

被引：5

作者：

Baranov, Anton D. ^{[1
,2
]}

Fedorovskiy, Konstantin Yu. ^{[1
,3
]}

机构：

[1] St Petersburg State Univ, St Petersburg, Russia

[2] Natl Res Univ, Higher Sch Econ, St Petersburg, Russia

[3] Bauman Moscow State Tech Univ, Moscow, Russia

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2017年 / 132卷

基金：

俄罗斯基础研究基金会;

关键词：

INTEGRAL MEANS SPECTRUM; UNIFORM APPROXIMATION;

D O I：

10.1007/s11854-017-0010-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the growth of the quantity a <<(T)|R'(z)|dm(z) for rational functions R of degree n which are bounded and univalent in the unit disk and prove that this quantity can grow like n (gamma) , gamma > 0, as n -> a. Some applications of this result to problems of regularity of boundaries of Nevanlinna domains are considered. We also discuss a related result of Dolzhenko, which applies to general (non-univalent) rational functions.

引用

页码：63 / 80

页数：18

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