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Criteria of convergence for quasiconformal mappings and their generalizations

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Abstract

We establish necessary and sufficient conditions for the convergence of normalized homeomorphisms of Sobolev class in terms of the Fourier transforms of complex characteristics in the case where the upper bound of dilations is exponentially bounded in measure. This allows us to construct various metrics generating locally uniform convergence of mappings.

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  1. V. I. Ryazanov
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Ryazanov, V.I. Criteria of convergence for quasiconformal mappings and their generalizations. Ukr Math J 48, 742–752 (1996). https://doi.org/10.1007/BF02384224

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  • DOI: https://doi.org/10.1007/BF02384224

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