Subharmonicity of vertical bar f vertical bar(p) for quasiregular harmonic functions, with applications

Abstract

We prove that if f is a quasiregular harmonic function, then there exists a number q is an element of (0, 1) such that vertical bar f vertical bar(q) is subharmonic, and use this fact to generalize a result of Rubel, Shields, and Taylor, and Tamrazov, on the moduli of continuity of holomorphic functions.