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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 2, Pages 422–432
DOI: https://doi.org/10.17377/smzh.2018.59.216 (Mi smj2983) 		 
The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev–Orlicz spaces

A. V. Menovshchikovabc

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Peoples' Friendship University of Russia, Moscow, Russia
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DOI: https://doi.org/10.17377/smzh.2018.59.216
Abstract: We determine the conditions under which the locally uniform limit of mappings generating bounded composition operators of Sobolev–Orlicz spaces also generates an operator of this kind. We estimate the distortion coefficient of the limit mapping.
Keywords: Sobolev–Orlicz space, distortion, codistortion, biting convergence, composition operator, $N$-function.
Funding agency Grant number
Russian Science Foundation 16-41-02004
The author was partially supported by the Russian Science Foundation (Grant 16-41-02004).
Received: 28.06.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 2, Pages 332–340
DOI: https://doi.org/10.1134/S0037446618020167
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.54
Language: Russian
Citation: A. V. Menovshchikov, “The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev–Orlicz spaces”, Sibirsk. Mat. Zh., 59:2 (2018), 422–432; Siberian Math. J., 59:2 (2018), 332–340
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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