Universal Teichmüller space and BMO

We first give some new characterizations on BMOA–Teichmuller space and various characterizations on VMOA–Teichmuller space as well. In particular, we prove that a quasisymmetric conformal welding h corresponds to an asymptotically smooth curve in the sense of Pommerenke (1978) [32] precisely when h is absolutely continuous with log h ′ ∈ VMO . We then show that these BMO–Teichmuller spaces have natural complex structures.