Integrable Teichmüller spaces for analysis on Weil-Petersson curves

The integrableTeichmüller space Tₚ for p 1 is defined by the p-integrability of Beltrami coefficients. We characterize a quasisymmetric homeomorphism h in Tₚ by the condition that h' belongs to the real p-Besov space, with a certain modification applied in the case p=1. This is done as part of the arguments for establishing a biholomorphic correspondence Λ from the product of Tₚ for simultaneous uniformization of p-Weil-Petersson curves into the p-Besov space. In particular, this proves the real-analytic equivalence between Tₚ and the real p-Besov space. Moreover, the Cauchy transform of Besov functions on Weil-Petersson curves can be expressed by the derivative of this holomorphic map Λ, and from this, the Calderón theorem in this setting is straightforward. It also follows that the Cauchy transforms on p-Weil-Petersson curves holomorphically depend on their embeddings as they vary in the Bers coordinates.