Authors: Arsenović, Miloš
Todorčević, Vesna 
Mateljević, Miodrag
Title: Lipschitz-type spaces and harmonic mappings in the space
Journal: Annales Academiae Scientiarum Fennicae Mathematica
Volume: 35
Issue: 1
First page: 379
Last page: 387
Issue Date: 20-Oct-2010
Rank: M21
ISSN: 1239-629X
DOI: 10.5186/aasfm.2010.3524
Abstract: 
We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u = P[ø] of a Lipschitz map ø: Sn-1 → 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.
Keywords: Harmonic mappings | Lipschitz-type spaces | Quasiregular mappings
Publisher: Academia Scientiarum Fennica
Project: MNTRS, Serbia, Grant No. 144020

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