Abstract
We prove that every quasiconformal mapping from the harmonic β-Bloch space between the unit ball and a spatial domain with C1 boundary is globally α-Hölder continuous for α<1−β, with the Hölder coefficient that does not depend neither on the mapping nor on β. An analogous result also holds for Lipschitz continuous, quasiconformal harmonic mappings for α<1. This is an approach towards the extension of some results from the complex plane obtained by Warschawski (1951) for conformal mappings and Kalaj (2022) for quasiconformal harmonic mappings.
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