Reshetnyak-classmappings and composition operators | Sciact - Система учета научной деятельности ИМ СО РАН

Reshetnyak-classmappings and composition operators Научная публикация

Журнал

Analysis and Mathematical Physics
ISSN: 1664-2368 , E-ISSN: 1664-235X

Вых. Данные

Год: 2025, Том: 15, Номер статьи : 143, Страниц : 27 DOI: 10.1007/s13324-025-01142-x

Ключевые слова

Metric space · Sobolev class · Composition operator · Carnot group · Distortion of a mapping · Generalized quasiconformal mapping

Авторы

Pavlov Stepan V. ¹ , Vodopyanov Sergey K. ²

Организации

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

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0006
2	Министерство науки и высшего образования РФ	075-15-2025-349

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.

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

Поступила в редакцию:	10 мая 2025 г.
Принята к публикации:	6 нояб. 2025 г.
Опубликована online:	13 нояб. 2025 г.

Web of science:	WOS:001614444100001
Scopus:	2-s2.0-105021825645
OpenAlex:	W7105673150

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