Extreme Points and Support Points of Families of Harmonic Bloch Mappings

被引：4
|
作者：
Deng, Hua [1 ]
Ponnusamy, Saminathan [2 ]
Qiao, Jinjing [1 ]
机构：
[1] Hebei Univ, Dept Math, Baoding 071002, Hebei, Peoples R China
[2] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India
来源：
POTENTIAL ANALYSIS | 2021年 / 55卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Bloch function; Harmonic Bloch mapping; Extreme point; Support point; Primary; Secondary; SUBORDINATION FAMILIES; UNIT BALL; COEFFICIENTS; STARLIKE;
D O I：
10.1007/s11118-020-09871-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the main aim is to discuss the existence of the extreme points and support points of families of harmonic Bloch mappings and little harmonic Bloch mappings. First, in terms of the Bloch unit-valued set, we prove a necessary condition for a harmonic Bloch mapping (resp. a little harmonic Bloch mapping) to be an extreme point of the unit ball of the normalized harmonic Bloch spaces (resp. the normalized little harmonic Bloch spaces) in the unit disk D. Then we show that a harmonic Bloch mapping f is a support point of the unit ball of the normalized harmonic Bloch spaces in D if and only if the Bloch unit-valued set of f is not empty. We also give a characterization for the support points of the unit ball of the harmonic Bloch spaces in D.
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页码：619 / 638
页数：20
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