NDLI: Equicontinuous classes of ring Q-homeomorphisms

Content Provider	Springer Nature Link
Author	Ryazav, V. I. Sevost’yav, E. A.
Copyright Year	2007
Abstract	We give a description of ring Q-homeomorphisms in ℝ$^{n}$, n ≥ 2, and find a series of conditions for normality of families of ring Q-homeomorphisms. For a family to be normal it is sufficient that the dominant Q(x) have logarithmic-type singularities of order at most n-1. Another sufficient condition for normality is that Q(x) has finite mean oscillation at each point; for example, Q(x) has finite mean value over infinitesimal balls. The definition of ring Q-homeomorphism is motivated by the ring definition of Gehring for quasiconformality. In particular, the mappings with finite length distortion satisfy a capacity inequality that justifies the definition of ring Q-homeomorphism. Therefore, deriving consequences of the theory to be presented, we obtain criteria for normality of families of homeomorphisms f with finite length distortion and homeomorphisms of the Sobolev class W loc 1,n in terms of the inner dilation K $_{ I }$ (x, f). Moreover, the class of strong ring Q-homeomorphisms for a locally summable Q is closed.
Starting Page	1093
Ending Page	1105
Page Count	13
File Format	PDF
ISSN	00374466
Journal	Siberian Mathematical Journal
Volume Number	48
Issue Number	6
e-ISSN	15739260
Language	English
Publisher	Springer US
Publisher Date	2007-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	normal family of mappings Q-homeomorphism finite mean oscillation mapping with finite distortion conformal mapping quasiconformal mapping Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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