Abstract
For \(\mu \in L^{\infty }(\Delta )\), the vector fields on the unit circle determined by \(\mu \) 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 \(\mu \). We show that those vector fields are not contained in the Sobolev class \(H^{3/2}\). 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.
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Supported by the Basic Scientific Research Foundation of Tianjin (Grant No. 2017KJ095) and the National Natural Science Foundation of China (Grant Nos. 11401432 and 11571172)
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Huo, S., Guo, H. On the non-smoothness of the vector fields for the dynamically invariant Beltrami coefficients. Arch. Math. 110, 377–389 (2018). https://doi.org/10.1007/s00013-018-1151-7
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DOI: https://doi.org/10.1007/s00013-018-1151-7