Harmonic automorphisms of the unit disk

✍ Scribed by Jan G. Krzyż; Maria Nowak

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 109 KB
• Volume: 105
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00019-9

✦ Synopsis

Let H be the class of harmonic automorphisms of the unit disk D. The function F =h-g associated with f =h+ g ∈ H maps D conformally onto a horizontally convex domain . Conversely, given both f ∈ H and F with F(D) = can be retrieved (Theorem 1). Compact subclasses H(M ) ⊂ H consisting of Poisson extensions of M -quasisymmetric automorphisms of @D span H (Lemma 1). For f(re it ) = +∞ n=-∞ cnr |n| e int ∈ H(M ) the bounds of |cn| (upper one for n = 0; 2, lower one for n = 1) and +∞ n=-∞ |cn| are given (Theorems 2-4).