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Toward the theory of ring Q-homeomophisms

Zhytomyr State University Library

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Relation http://eprints.zu.edu.ua/13801/
 
Title Toward the theory of ring Q-homeomophisms
 
Creator Севостьянов, Е. А.
Рязанов, В.
 
Subject Mathematical Analysis
 
Description We investigate classes of the so-called ring Q-homeomorphisms including,
in particular, Q-homeomorphisms, various classes of homeomorphisms
with finite length distortion, Sobolev’s classes etc. In terms of the majorant
Q(x), we give a series of criteria for normality based on estimates of
the distortion of the spherical distance under ring Q-homeomorphisms. In
particular, it is shown that the class f of a domain D � Rn into Rn, n � 2, with h(Rn\f(D)) � � > 0, forms
a normal family, if Q(x) has finite mean oscillation in D. We also prove
normality of type whose degrees are not greater than n − 1 at every point x 2 D.
The results are applicable, in particular, to mappings with finite length
distortion and Sobolev’s classes.
 
Date 2008
 
Type Article
PeerReviewed
 
Format text
 
Language uk
english
 
Identifier http://eprints.zu.edu.ua/13801/1/05_Ryazanov.pdf
Севостьянов, Е. А. and Рязанов, В. (2008) Toward the theory of ring Q-homeomophisms. Israel Journal of Mathematics (168). pp. 101-118.