Introduction of a complex structure on the p-integrable Teichmüller space

For p 1, the p-integrable Teichmller space is the metric subspace of the Teichmller space composed of the Teichmller equivalence classes with p-integrable Beltrami coefficient. In this paper, for p 2, we introduce a complex structure on the p-integrable Teichmller space of an arbitrary Fuchsian group satisfying a certain geometric condition. As an application, we show the coincidence of two canonical distances on the metric subspace.