On Orlicz-Sobolev classes on factor spaces

TL;DR

This paper investigates the properties of Orlicz-Sobolev classes on factor spaces derived from the unit ball in higher dimensions, providing distortion estimates and boundary behavior theorems for these mappings.

Contribution

It introduces new distortion estimates and boundary behavior theorems for Orlicz-Sobolev classes on factor spaces under M"{o}bius transformations.

Findings

Distortion estimates of the modulus of sphere families

Theorems on local behavior of Orlicz--Sobolev mappings

Results on boundary behavior of mappings

Abstract

We study the factor-spaces of the unit ball of dimension, not less than three, by a certain group of M\"{o}bius transformations. For mappings of such spaces, an estimate of the distortion of the modulus of families of spheres is obtained. As applications, we obtain theorems on the locally and boundary behavior of the Orlicz--Sobolev classes between factor spaces.