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Estimates on μ(z)-homeomorphisms of the unit disk

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Abstract

In the theory ofK-quasiconformal mappings, Mori's theorem shows thatK-quasiconformal mappings on the unit disk satisfy the Hölder condition, where the coefficient 16 is best possible. In this paper, we prove that self-μ(z)-homeomorphisms on the unit disk have an analogical result to Mori's theorem when the integral mean dilatations are controlled by log function. An unimprovable inequality is obtained.

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Authors and Affiliations

  1. Department of Mathematics, XiXi Campus, Zhejiang University, Hangzhou, 310028, Zhejiang, P. R. China

    Chen Zhiguo

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  1. Chen Zhiguo
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Correspondence to Chen Zhiguo.

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Zhiguo, C. Estimates on μ(z)-homeomorphisms of the unit disk. Isr. J. Math. 122, 347–358 (2001). https://doi.org/10.1007/BF02809907

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  • DOI: https://doi.org/10.1007/BF02809907

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