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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 5, Pages 1137–1149
DOI: https://doi.org/10.33048/smzh.2022.63.514
(Mi smj7719)
 

This article is cited in 1 scientific paper (total in 1 paper)

Grand Sobolev spaces on metric measure spaces

S. Pavlov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (320 kB) Citations (1)
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Abstract: We study the properties of the so-called grand Sobolev spaces on a metric measure space. The introduction of the spaces is motivated by the available pointwise description of the elements of the spaces in the Euclidean case. We obtain a continuous embedding of the grand Sobolev space into a space of integrable functions under some regularity condition on the metric measure space.
Keywords: grand Lebesgue spaces, grand Sobolev spaces, regular metric measure spaces.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–281 on April 5, 2022 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 28.11.2021
Revised: 05.02.2022
Accepted: 10.02.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 5, Pages 956–966
DOI: https://doi.org/10.1134/S0037446622050147
Document Type: Article
UDC: 517.518
MSC: 35R30
Language: Russian
Citation: S. Pavlov, “Grand Sobolev spaces on metric measure spaces”, Sibirsk. Mat. Zh., 63:5 (2022), 1137–1149; Siberian Math. J., 63:5 (2022), 956–966
Citation in format AMSBIB
\Bibitem{Pav22}
\by S.~Pavlov
\paper Grand Sobolev spaces on metric measure spaces
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 5
\pages 1137--1149
\mathnet{http://mi.mathnet.ru/smj7719}
\crossref{https://doi.org/10.33048/smzh.2022.63.514}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 5
\pages 956--966
\crossref{https://doi.org/10.1134/S0037446622050147}
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