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Sibirskii Matematicheskii Zhurnal, 2025, Volume 66, Number 5, Pages 951–969
DOI: https://doi.org/10.33048/smzh.2025.66.515 (Mi smj7991) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Composition operators between Sobolev spaces on metric measure spaces. I

D. A. Sboev

Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2025.66.515
Abstract: We obtain a description of homeomorphisms inducing bounded composition operators between Sobolev spaces whose functions are defined on metric measure spaces. As a consequence, we establish a characterization of quasiconformal mappings in metric measure spaces.
Keywords: composition operator, metric measure space, Sobolev space, ${\mathcal Q}_{p}$-homeomorphism, mapping of finite distortion, quasiconformal mapping.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2025-349
The work was supported by the Mathematical Center in Akademgorodok under agreement 075–15–2025–349 dated April 29, 2025 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 24.06.2025
Revised: 24.06.2025
Accepted: 03.07.2025
English version:
Siberian Mathematical Journal, 2025, Volume 66, Issue 5, Pages 1254–1269
DOI: https://doi.org/10.1134/S0037446625050155
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: D. A. Sboev, “Composition operators between Sobolev spaces on metric measure spaces. I”, Sibirsk. Mat. Zh., 66:5 (2025), 951–969; Siberian Math. J., 66:5 (2025), 1254–1269
Citation in format AMSBIB
\Bibitem{Sbo25}
\by D.~A.~Sboev
\paper Composition operators between~Sobolev~spaces on~metric measure spaces.~I
\jour Sibirsk. Mat. Zh.
\yr 2025
\vol 66
\issue 5
\pages 951--969
\mathnet{http://mi.mathnet.ru/smj7991}
\transl
\jour Siberian Math. J.
\yr 2025
\vol 66
\issue 5
\pages 1254--1269
\crossref{https://doi.org/10.1134/S0037446625050155}
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