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For $$\mu \in L^{\infty }(\Delta )$$μ∈L∞(Δ), the vector fields on the unit circle determined by $$\mu $$μ play an important role in the theory of the universal Teichmüller space. The… Click to show full abstract
For $$\mu \in L^{\infty }(\Delta )$$μ∈L∞(Δ), the vector fields on the unit circle determined by $$\mu $$μ play an important role in the theory of the universal Teichmüller space. The aim of this paper is to give some characterizations of the vector fields induced by dynamically invariant $$\mu $$μ. We show that those vector fields are not contained in the Sobolev class $$H^{3/2}$$H3/2. At last, we give some results on dynamically invariant vectors to show that the vector fields, the quasi-symmetric homeomorphisms, and the quasi-circles are closely related.
Journal Title: Archiv der Mathematik
Year Published: 2018
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