Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 265-276
Huaqiao University, Department of Mathematics
Quanzhou, Fujian, 362021, P.R. China; chenmmi 'at' hqu.edu.cn
Huaqiao University, Department of Mathematics
Quanzhou, Fujian, 362021, P.R. China; chxtt 'at' hqu.edu.cn
Abstract. paper we show that (K,K')-quasiconformal mappings with unbounded image domains are not Hölder continuous, which is different from the case with bounded image domains given by Kalaj and Mateljevic. For a (K,K')-quasiconformal harmonic mapping of the upper half plane onto itself, we prove that it is Lipschitz and hyperbolically Lipschitz continuous. Moreover, we get four equivalent conditions for a harmonic mapping of the upper half plane onto itself to be a (K,K')-quasiconformal mapping.
2010 Mathematics Subject Classification: Primary 30C65; Secondary 30C62.
Key words: Harmonic mappings, (K,K')-quasiconformal mappings, Lipschitz continuity, Hilbert transformations.
Reference to this article: M. Chen and X. Chen: (K,K')-Quasiconformal harmonic mappings of the upper half plane onto itself. Ann. Acad. Sci. Fenn. Math. 37 (2012), 265-276.
doi:10.5186/aasfm.2012.3716
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