An extremal problem for harmonic self-mappings of the unit disk

Abstract

Let Aut H (D) be the class of harmonic automorphisms of the unit disk D. For f (re iϕ ) = ∞ n=−∞ c n r |n| e inϕ ∈ Aut H (D) the upper bounds of Re n k=1 {c k + c −k } are given.