QUASICONFORMAL EXTENSION OF MEROMORPHIC FUNCTIONS WITH NONZERO POLE

被引：10

作者：

Bhowmik, B. ^{[1
]}

Satpati, G. ^{[1
]}

Sugawa, T. ^{[2
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

[2] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 06期

关键词：

Quasiconformal map; convolution;

D O I：

10.1090/proc/12933

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we consider meromorphic univalent functions f(z) in the unit disc with a simple pole at z = p is an element of (0, 1) which have a k-quasiconformal extension to the extended complex plane (C) over cap, where 0 <= k < 1. We denote the class of such functions by Sigma(k)(p). We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at z = p is an element of(0, 1) to belong to the class Sigma(k)(p). Finally, we give a convolution property for functions in the class Sigma(k)(p).

引用

页码：2593 / 2601

页数：9