Properties of a Class of p -Harmonic Functions

Abstract

A $p$ times continuously differentiable complex-valued function $F=u+iv$ in a domain $D\subseteq ℂ$ is $p$-harmonic if $F$ satisfies the $p$-harmonic equation $\mathrm{\Delta }\cdots \mathrm{\Delta }F=0$, where $p$ is a positive integer. By using the generalized Salagean differential operator, we introduce a class of $p$-harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.