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New Properties of Composition Operators in Sobolev Spaces on Riemannian Manifolds Научная публикация

Журнал

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Вых. Данные

Год: 2025, Том: 66, Номер: 4, Страницы: 914-927 Страниц : 14 DOI: 10.1134/s0037446625040044

Ключевые слова

Riemannian space, class of Sobolev mappings with values in a metric space, approximate differentiability, distortion of a mapping, generalized quasiconformal mapping, composition operator

Авторы

Vodopyanov S.K. ¹

Организации

1	Sobolev Institute of Mathematics

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0006

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.

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

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

Поступила в редакцию:	4 апр. 2025 г.
Принята к публикации:	26 мая 2025 г.
Опубликована в печати:	23 июл. 2025 г.
Опубликована online:	23 июл. 2025 г.

Web of science:	WOS:001535187000002
Scopus:	2-s2.0-105011258064
РИНЦ:	82650975
OpenAlex:	W4412610240

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