This article is cited in 5 papers

On Local Properties of Spatial Generalized Quasi-isometries

R. R. Salimov^a, E. A. Sevost'yanov<sup>b

a</sup> Institute of Mathematics, Ukrainian National Academy of Sciences
^b Zhytomyr I. Franko State University

Abstract: An upper bound for the measure of the image of a ball under mappings of a certain class generalizing the class of branched spatial quasi-isometries is determined. As a corollary, an analog of Schwarz' classical lemma for these mappings is proved under an additional constraint of integral character. The obtained results have applications to the classes of Sobolev and Orlicz–Sobolev spaces.

Keywords: mappings with bounded and finite distortion, local behavior of mappings, equicontinuity, bounds for distance distortion.

UDC: 517.5

Received: 22.01.2015
Revised: 15.08.2016

DOI: 10.4213/mzm10707

 English version: Mathematical Notes, 2017, 101:4, 704–717

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