On extension of some generalizations of quasiconformal mappings to a boundary

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.