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

Let AutH (D) be the class of harmonic automorphisms of the unit disk D. For f (reiϕ) = ∞n=−∞ cnr|n|einϕ ∈ AutH (D) the upper bounds of Re n k=1{ck + c−k} are given. © 2006 Elsevier Inc. All rights reserved