The Schwarz Type Inequality for Harmonic Mappings of the Unit Disc with Boundary Normalization

被引：4

作者：

Partyka, Dariusz ^{[1
,2
]}

Zajac, Jozef ^{[1
]}

机构：

[1] State Sch Higher Educ Chelm, Inst Math & Informat Technol, PL-22100 Chelm, Poland

[2] John Paul II Catholic Univ Lublin, Inst Math & Comp Sci, PL-20950 Lublin, Poland

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2015年 / 9卷 / 01期

关键词：

Harmonic mappings; Poisson integral; Schwarz Lemma;

D O I：

10.1007/s11785-014-0398-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H be the class of all complex-valued harmonic functions F of the unit disk D into itself such that for every k is an element of {0, 1, 2} and almost every z is an element of T-k := {e(i theta) : 2k pi/3 < theta < 2(k + 1)pi/3} the radial limit of F at z belongs to the angular sector determined by the convex hull spanned by the origin and arc T-k. The sharp estimation of the modulus vertical bar F(z)vertical bar for z is an element of D in the class H is obtained and the extremal functions are determined.

引用

页码：213 / 228

页数：16