2018
Том 70
№ 9

# On extension of some generalizations of quasiconformal mappings to a boundary

Lomako T.V.

Abstract

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 $f: D → D’$ with $Q ∈ L_1(D)$; 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.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 10, pp 1568-1577.

Citation Example: Lomako T.V. On extension of some generalizations of quasiconformal mappings to a boundary // Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1329-1337.

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