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On the modulus of continuity of harmonic quasiregular mappings on the unit ball in Rn

Arsenović Miloš (Faculty of Mathematics, Belgrade)
Manojlović Vesna (Faculty of Organizational Sciences, Belgrade)

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