Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 379-387

LIPSCHITZ-TYPE SPACES AND HARMONIC MAPPINGS IN THE SPACE

Milos Arsenovic, Vesna Manojlovic and Miodrag Mateljevic

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, Belgrade, Serbia; arsenovic 'at' matf.bg.ac.yu

University of Belgrade, Faculty of Organizational Sciences
Jove Ilica 154, Belgrade, Serbia; vesnak 'at' fon.bg.ac.yu

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, Belgrade, Serbia; miodrag 'at' matf.bg.ac.yu

Abstract. We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u = P[\phi] of a Lipschitz map \phi : S^n-1 \to Rⁿ. We also consider additional conditions which provide that u is Lipschitz on the unit ball; in particular, we give characterizations of Lipschitz continuity of u in the planar case and in the upper half space setting. We also answer a question posed by Martio in [OM] and extend this to the case of several variables.

2000 Mathematics Subject Classification: Primary 30C80, 30C62; Secondary 30C55, 30H05.

Key words: Lipschitz-type spaces, harmonic mappings, quasiregular mappings.

Reference to this article: M. Arsenovic, V. Manojlovic and M. Mateljevic: Lipschitz-type spaces and harmonic mappings in the space. Ann. Acad. Sci. Fenn. Math. 35 (2010), 379-387.

Full document as PDF file

doi:10.5186/aasfm.2010.3524