Authors: Arsenović, Miloš
Todorčević, Vesna 
Title: On the modulus of continuity of harmonic quasiregular mappings on the unit ball in Rn
Journal: Filomat
Volume: 23
Issue: 3
First page: 199
Last page: 202
Issue Date: 2009
Rank: M23
ISSN: 0354-5180
DOI: 10.2298/FIL0903199A
We show that, for a class of moduli functions ω(δ), 0 ≤ δ ≤ 2, the property ׀φ(ξ) - φ(η) ׀≤ ω (׀ξ - η׀), ξ, ηЄ Sn-1 implies the corresponding property ׀u(x)-u(y) ׀≤ Cω(׀x-y׀) x, y Є Bn; for u = P[φ], provided u is a quasiregular mapping. Our class of moduli functions includes φ(δ) = δα (0 < α ≤ 1), so our result generalizes earlier results on Hölder continuity (see [1]) and Lipschitz continuity (see [2]).
Keywords: quasihyperbolic metric | bilipschitz maps
Publisher: Faculty of Sciences and Mathematics, University of Niš

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