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August 2020 Extreme points and support points of harmonic $\alpha$-Bloch mappings
Miaomiao Huang, Saminathan Ponnusamy, Jinjing Qiao
Rocky Mountain J. Math. 50(4): 1323-1354 (August 2020). DOI: 10.1216/rmj.2020.50.1323

Abstract

We consider the problem of existence of the extreme points and support points of harmonic α-Bloch mappings and little harmonic α-Bloch mappings. First, we prove a necessary condition for a little harmonic α-Bloch mapping to be an extreme point of the unit ball of the normalized little harmonic α-Bloch spaces in the unit disk 𝔻, and we also show that a harmonic α-Bloch unit-valued set consists of several simple closed pairwise disjoint analytic curves and several isolated points. Then we show that a harmonic α-Bloch mapping f is a support point of the unit ball of the normalized harmonic α-Bloch spaces in 𝔻 if and only if the α-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 α-Bloch spaces in 𝔻.

Citation

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Miaomiao Huang. Saminathan Ponnusamy. Jinjing Qiao. "Extreme points and support points of harmonic $\alpha$-Bloch mappings." Rocky Mountain J. Math. 50 (4) 1323 - 1354, August 2020. https://doi.org/10.1216/rmj.2020.50.1323

Information

Received: 4 October 2019; Revised: 28 January 2020; Accepted: 1 February 2020; Published: August 2020
First available in Project Euclid: 29 September 2020

zbMATH: 07261867
MathSciNet: MR4154810
Digital Object Identifier: 10.1216/rmj.2020.50.1323

Subjects:
Primary: 30D45 , 30H30 , 31A05
Secondary: ‎46E15

Keywords: Bloch function , extreme point , harmonic $\alpha$-Bloch mapping , harmonic Bloch mapping , little Bloch functions , little harmonic $\alpha$-Bloch mapping , support point

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 4 • August 2020
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