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On extension of some generalizations of quasiconformal mappings to a boundary

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Ukrainian Mathematical Journal Aims and scope

This work is devoted to the investigation of ring Q-homeomorphisms. We formulate conditions for a function Q(x) and the boundary of a domain under which every ring Q-homeomorphism admits a homeomorphic extension to the boundary. For an arbitrary ring Q-homeomorphism f: DD’ with QL 1(D); we study the problem of the extension of inverse mappings to the boundary. It is proved that an isolated singularity is removable for ring Q-homeomorphisms if Q has finite mean oscillation at a point.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 10, pp. 1329–1337, October, 2009.

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Lomako, T.V. On extension of some generalizations of quasiconformal mappings to a boundary. Ukr Math J 61, 1568–1577 (2009). https://doi.org/10.1007/s11253-010-0298-6

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  • DOI: https://doi.org/10.1007/s11253-010-0298-6

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