On boundary extension of one class of mappings in terms of prime ends

E.A. Sevost'yanov; S. A.  Skvortsov; I.A. Sverchevska

doi:10.30970/ms.53.1.29-40

E.A. Sevost'yanov Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
S. A. Skvortsov Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
I.A. Sverchevska Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

DOI: https://doi.org/10.30970/ms.53.1.29-40

Keywords: metric spaces, quasiconformal mappings, mappings with bounded and nite distortion, equiconti- nuity, moduli of families of paths

Abstract

Here we consider the classes of mappings of metric spaces that distort the modulus of families of paths similarly to Poletsky inequality. For domains, which are not locally connected at the boundaries, we obtain results on the boundary extension of the indicated mappings. We also investigate the local and global behavior
of mappings in the context of the equicontinuity of their families. The main statements of the article are proved under the condition that the majorant responsible for the distortion of the modulus of the families of paths has a finite mean oscillation at the corresponding points. The results are applicable to well-known classes of conformal and quasiconformal mappings as well as mappings with a finite distortion.

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