BMO-Teichmüller spaces revisited

In [6] the equivalence among three definitions of BMO-Teichmüller spaces associated with a Fuchsian group was proven using the Douady-Earle extension operator. In this paper, we show that these equivalences are actually biholomorphisms. In [6] it was further shown that the Douady-Earle extension operator is continuous at the origin. We improve this result by showing Gâteaux-differentiability at this point.