On some local properties of space generalized quasiisometries

TL;DR

This paper investigates a class of generalized quasiisometries, providing measure estimates for images of balls and establishing an analog of Schwartz lemma, with applications in Sobolev and Orlicz–Sobolev spaces.

Contribution

It introduces upper measure estimates and a Schwartz lemma analog for generalized quasiisometries, extending their analysis in Sobolev and Orlicz–Sobolev contexts.

Findings

Derived upper bounds for measures of images of balls under these mappings

Established an analog of Schwartz lemma for the class of mappings

Applied results to Sobolev and Orlicz–Sobolev function spaces

Abstract

For some class of mappings, which are generalization of space quasiisometries, an upper estimate for a measure of image of a ball is obtained. As consequence, it is obtained one analog of Schwartz lemma for mappings mentioned above. Results of the paper are applicable in Sobolev and Orlicz--Sobolev classes.