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

Abstract

We show that, for a class of moduli functions ?(?), 0 ? ? ? 2, the property ??(?) - ?(?) ?? ? (?? - ??), ?, ?? Sn-1 implies the corresponding property ?u(x)-u(y) ?? C?(?x-y?) x, y ? Bn; for u = P[?], provided u is a quasiregular mapping. Our class of moduli functions includes ?(?) = ?? (0 < ? ? 1), so our result generalizes earlier results on H?lder continuity (see [1]) and Lipschitz continuity (see [2]).