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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 460–483
DOI: https://doi.org/10.33048/semi.2022.19.040 (Mi semr1515) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Real, complex and functional analysis

On the continuity of Sobolev-type functions on homogeneous metric spaces

A. S. Romanovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.040
Abstract: On $s$-homogeneous metric spaces with measure for Sobolev-type functions with "smoothness" $\alpha \le 1$ we prove the property $s/\alpha$- absolute continuity, in the case when the characteristics that define "smoothness" belong to the corresponding Lorentz space.
Keywords: Lorentz space, Sobolev type functions, homogeneous metric spaces, absolute continuity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0007
Received April 25, 2022, published August 19, 2022
Document Type: Article
UDC: 517.51
MSC: 46E35
Language: Russian
Citation: A. S. Romanov, “On the continuity of Sobolev-type functions on homogeneous metric spaces”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 460–483
Citation in format AMSBIB
\Bibitem{Rom22}
\by A.~S.~Romanov
\paper On the continuity of Sobolev-type functions on homogeneous metric spaces
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 460--483
\mathnet{http://mi.mathnet.ru/semr1515}
\crossref{https://doi.org/10.33048/semi.2022.19.040}
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