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Reshetnyak-classmappings and composition operators Full article

Journal Analysis and Mathematical Physics
ISSN: 1664-2368 , E-ISSN: 1664-235X
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 Pavlov Stepan V. 1 , Vodopyanov Sergey K. 2
Affiliations
1 Department of Mechanics and Mathematics, Novosibirsk State University, 1 Pirogov St, 630090 Novosibirsk, Russian Federation
2 Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Akademika Koptyuga Pr, 630090 Novosibirsk, Russian Federation

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
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: Пока нет цитирований
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