Dirichlet and VMOA domains via Schwarzian derivative (Q837587)

Let \(g: \mathbb{D}\to \Omega\) be a bounded conformal mapping of the unit disk onto a Jordan domain. The authors establish in terms of the Schwarzian derivative necessary and sufficient conditions for \(\log g'(z)\) to belong to various spaces (Besov, Dirichlet, VMOA). The results complete in part a theorem from the monograph of \textit{J. B. Garett} and \textit{D. E. Marshall} [Harmonic measure. Paperback reprint of the hardback edition 2005. New Mathematical Monographs 2. Cambridge: Cambridge University Press (2005; Zbl 1139.31001)] and recent results of \textit{J. Pau} and \textit{J. A. Peláez} [J. Math. Anal. Appl. 350, 184--194 (2009; Zbl 1159.30011)].