Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 567-576

ON PLANAR HARMONIC LIPSCHITZ AND PLANAR HARMONIC HARDY CLASSES

Shaolin Chen, Saminathan Ponnusamy and Xiantao Wang

Hunan Normal University, Department of Mathematics
Changsha, Hunan 410081, P.R. China; shlchen1982 'at' yahoo.com.cn

Indian Institute of Technology Madras, Department of Mathematics
Chennai-600 036, India; samy 'at' iitm.ac.in

Hunan Normal University, Department of Mathematics
Changsha, Hunan 410081, P.R. China; xtwang 'at' hunnu.edu.cn

Abstract. In this paper, we investigate the properties of two classes of planar harmonic mappings. First, we discuss the equivalent norms on Lipschitz-type spaces of harmonic K-quasiregular mappings and then we study the relationship between the harmonic area functions and the harmonic Hardy classes. We also establish Landau's theorem for a class of harmonic Hardy mappings.

2010 Mathematics Subject Classification: Primary 30C65, 30C45; Secondary 30C20.

Key words: Harmonic quasiregular mapping, Lipschitz-type space, harmonic Hardy class, univalent functions, Landau's theorem.

Reference to this article: S. Chen, S. Ponnusamy and X. Wang: On planar harmonic Lipschitz and planar harmonic Hardy classes. Ann. Acad. Sci. Fenn. Math. 36 (2011), 567-576.

Full document as PDF file

doi:10.5186/aasfm.2011.3640

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