Integrable Teichmüller space

This paper deals with the p-integrable Teichmüller space and gives an intrinsic characterization of a p-integrable asymptotic affine homeomorphism for p>2. More precisely, it is proved that a sense-preserving homeomorphism h on the unit circle is p-integrable asymptotic affine, namely, h can be extended to a quasiconformal mapping to the unit disk whose Beltrami coefficient is p-integrable in the Poincaré metric if and only if h is absolutely continuous such that log⁡h′ belongs to the Besov class Bp(S1).