Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 37, 2012, 69-79
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 some properties of planar harmonic mappings in Hardy spaces. First, we discuss the integral means of harmonic mappings and those of their derivatives, and as a consequence, we solve the open problem of Girela and Peláez in the setting of harmonic mappings. In addition, we establish coefficient estimates and a distortion theorem for harmonic mappings in Hardy spaces.
2010 Mathematics Subject Classification: Primary 30C65, 30C45; Secondary 30C20.
Key words: Harmonic mapping, harmonic Hardy space, coefficient estimate.
Reference to this article: S. Chen, S. Ponnusamy and X. Wang: Integral means and coefficient estimates on planar harmonic mappings. Ann. Acad. Sci. Fenn. Math. 37 (2012), 69-79.
doi:10.5186/aasfm.2012.3707
Copyright © 2012 by Academia Scientiarum Fennica