a Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain b University of Joensuu, Department of Physics and Mathematics, PO Box 111, 80101 Joensuu, Finland
Abstract:
Short proofs of the following results concerning a bounded conformal map g of the unit disc D are presented: (1) logg′ belongs to the Dirichlet space if and only if the Schwarzian derivative Sg of g satisfies Sg(z)(1−2|z|)∈L2(D); (2) logg′∈VMOA if and only if 2|Sg(z)|3(1−2|z|) is a vanishing Carleson measure on D. Analogous results for Besov and Qp,0 spaces are also given.
