Some notes on quasisymmetric flows of Zygmund vector fields

In an important paper [24], Reimann showed that the flow mappings of a continuous vector field of Zygmund class Λ⁎ are quasisymmetric homeomorphisms. In this paper, we will discuss the flow mappings when the vector field belongs to the smooth Zygmund class λ⁎ or the Sobolev class H32.