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Mat. Zametki, 2017, Volume 101, Issue 4, Pages 594–610 (Mi mz10707)  

On Local Properties of Spatial Generalized Quasi-isometries

R. R. Salimova, E. A. Sevost'yanovb

a 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.

DOI: https://doi.org/10.4213/mzm10707

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

Bibliographic databases:

UDC: 517.5
Received: 22.01.2015
Revised: 15.08.2016

Citation: R. R. Salimov, E. A. Sevost'yanov, “On Local Properties of Spatial Generalized Quasi-isometries”, Mat. Zametki, 101:4 (2017), 594–610; Math. Notes, 101:4 (2017), 704–717

Citation in format AMSBIB
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