Moduli of Continuity of Harmonic Quasiregular Mappings in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{B}^n$\end{document}

We prove that ωu(δ) ≤ Cωf(δ), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u : \overline{\mathbb{B}^n} \rightarrow \mathbb{R}^n$\end{document} is the harmonic extension of a continuous map \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f:\mathbb{S}^{n-1}\rightarrow\mathbb{R}^n$\end{document}, if u is a K-quasiregular map. Here C is a constant depending only on n, ωf and K and ωh denotes the modulus of continuity of h.