Reshetnyak-classmappings and composition operators Full article
| Journal |
Analysis and Mathematical Physics
ISSN: 1664-2368 , E-ISSN: 1664-235X |
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| Output data | Year: 2025, Volume: 15, Article number : 143, Pages count : 27 DOI: 10.1007/s13324-025-01142-x | ||||
| Tags | Metric space · Sobolev class · Composition operator · Carnot group · Distortion of a mapping · Generalized quasiconformal mapping | ||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
| 2 | Министерство науки и высшего образования РФ | 075-15-2025-349 |
Abstract:
For the Reshetnyak-class homeomorphisms ϕ : U→ Y , where U is a domain in
some Carnot group and Y is a metric space, we obtain an equivalent description as the
homeomorphisms which induce the bounded composition operator
ϕ^∗ : Lip(Y ) → L^1_q (U),
where 1 ≤ q ≤ ∞, as ϕ∗u = u ◦ ϕ for u ∈ Lip(Y ). We demonstrate the utility of our
approach by characterizing the homeomorphisms ϕ : U → U' of domains in some
Carnot group G which induce the bounded composition operator
ϕ^∗ : L^1_p( U') ∩ Lip_{loc}( U') → L^1_q (U), 1 ≤ q ≤ p ≤ ∞,
on homogeneous Sobolev spaces. The new proof of this known criterion is much
shorter than the one already available, requires a minimum of tools, and enables us to
obtain new properties of the homeomorphisms in question.
Cite:
Pavlov S.V.
, Vodopyanov S.K.
Reshetnyak-classmappings and composition operators
Analysis and Mathematical Physics. 2025. V.15. 143 :1-27. DOI: 10.1007/s13324-025-01142-x WOS Scopus OpenAlex
Reshetnyak-classmappings and composition operators
Analysis and Mathematical Physics. 2025. V.15. 143 :1-27. DOI: 10.1007/s13324-025-01142-x WOS Scopus OpenAlex
Dates:
| Submitted: | May 10, 2025 |
| Accepted: | Nov 6, 2025 |
| Published online: | Nov 13, 2025 |
Identifiers:
| Web of science: | WOS:001614444100001 |
| Scopus: | 2-s2.0-105021825645 |
| OpenAlex: | W7105673150 |
Citing:
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