Properties of a Class of p-Harmonic Functions

Abstract EN

A p times continuously differentiable complex-valued function F=u+iv in a domain D⊆ℂ is p-harmonic if F satisfies the p-harmonic equation Δ⋯ΔF=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.