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ON HARMONIC BLOCH SPACES IN THE UNIT BALL OF ℂn

Part of: Geometric function theory

Published online by Cambridge University Press:  10 June 2011

SH. CHEN  and
X. WANG
SH. CHEN
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China (email: shlchen1982@yahoo.com.cn)
X. WANG*
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China (email: xtwang@hunnu.edu.cn)
*
✉For correspondence; e-mail: xtwang@hunnu.edu.cn
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Abstract

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In this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball 𝔹n. First, we characterize the harmonic Bloch spaces and the little harmonic Bloch spaces from 𝔹n to ℂ in terms of weighted Lipschitz functions. Then we prove the existence of a Landau–Bloch constant for a class of vector-valued harmonic Bloch mappings from 𝔹n to ℂn.

Keywords

harmonic Bloch spacelittle harmonic Bloch spaceweighted Lipschitz functioncharacterization

MSC classification

Secondary: 30C65: Quasiconformal mappings in $^n$, other generalizations 30C20: Conformal mappings of special domains
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 67 - 78
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research was partly supported by NSF of China (No. 11071063), Hunan Provincial Innovation Foundation for Postgraduate (No. 125000-4113) and the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.

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