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LANDAU’S THEOREM AND MARDEN CONSTANT FOR HARMONIC ν-BLOCH MAPPINGS

Part of: Geometric function theory

Published online by Cambridge University Press:  10 June 2011

SH. CHEN ,
S. PONNUSAMY  and
X. WANG
SH. CHEN
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China (email: shlchen1982@yahoo.com.cn)
S. PONNUSAMY
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India (email: samy@iitm.ac.in)
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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Our main aim is to investigate the properties of harmonic ν-Bloch mappings. Firstly, we establish coefficient estimates and a Landau theorem for harmonic ν-Bloch mappings, which are generalizations of the corresponding results in Bonk et al. [‘Distortion theorems for Bloch functions’, Pacific. J. Math.179 (1997), 241–262] and Chen et al. [‘Bloch constants for planar harmonic mappings’, Proc. Amer. Math. Soc.128 (2000), 3231–3240]. Secondly, we obtain an improved Landau theorem for bounded harmonic mappings. Finally, we obtain a Marden constant for harmonic mappings.

Keywords

harmonic mappingharmonic ν-Bloch mappingsubordinationcoefficient estimateLandau’s theorem

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. 19 - 32
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.

References

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