Subharmonicity of |f |p for quasiregular harmonic functions, with applications

We prove that if f is a quasiregular harmonic function, then there exists a number q ∈ (0, 1) such that |f |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. © 2007 Elsevier Inc. All rights reserved.