New Properties of Composition Operators in Sobolev Spaces on Riemannian Manifolds Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2025, Volume: 66, Number: 4, Pages: 914-927 Pages count : 14 DOI: 10.1134/s0037446625040044 | ||
| Tags | Riemannian space, class of Sobolev mappings with values in a metric space, approximate differentiability, distortion of a mapping, generalized quasiconformal mapping, composition operator | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
An equivalent description is obtained for homeomorphisms ϕ of a domain Ω in a Riemannian space M onto a metric space Y, which guarantees the boundedness of the composition operator from the space of Lipschitz functions Lip(Y) into the homogeneous Sobolev space on M with first generalized derivatives integrable to the power 1 ≤ q ≤ ∞, along with other new properties of such homeomorphisms. The new approach makes it possible to effectively prove a theorem on homeomorphisms of domains in an arbitrary Riemannian space M that induce a bounded composition operator between Sobolev spaces with first generalized derivatives. The new proof, which is considerably shorter compared to the original one, relies on a minimal set of tools and allows us to establish new properties of the homeomorphisms under study.
Cite:
Vodopyanov S.K.
New Properties of Composition Operators in Sobolev Spaces on Riemannian Manifolds
Siberian Mathematical Journal. 2025. V.66. N4. P.914-927. DOI: 10.1134/s0037446625040044 WOS Scopus РИНЦ OpenAlex
New Properties of Composition Operators in Sobolev Spaces on Riemannian Manifolds
Siberian Mathematical Journal. 2025. V.66. N4. P.914-927. DOI: 10.1134/s0037446625040044 WOS Scopus РИНЦ OpenAlex
Original:
Водопьянов С.К.
Новые свойства операторов композиции в пространствах Соболева на римановых многообразиях
Сибирский математический журнал. 2025. Т.66. №4. С.596-612. DOI: 10.33048/smzh.2025.66.404 РИНЦ
Новые свойства операторов композиции в пространствах Соболева на римановых многообразиях
Сибирский математический журнал. 2025. Т.66. №4. С.596-612. DOI: 10.33048/smzh.2025.66.404 РИНЦ
Dates:
| Submitted: | Apr 4, 2025 |
| Accepted: | May 26, 2025 |
| Published print: | Jul 23, 2025 |
| Published online: | Jul 23, 2025 |
Identifiers:
| Web of science: | WOS:001535187000002 |
| Scopus: | 2-s2.0-105011258064 |
| Elibrary: | 82650975 |
| OpenAlex: | W4412610240 |
Citing:
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