TY - JOUR

T1 - Reshetnyak-class mappings and composition operators

AU - Pavlov, Stepan V.

AU - Vodopyanov, Sergey K.

N1 - S. V. Pavlov: The work is supported by the Mathematical Center in Akademgorodok under the Agreement 075–15–2025–349 with the Ministry of Science and Higher Education of the Russian Federation. S. K. Vodopyanov: Working in the framework of the State Task to the Sobolev Institute of Mathematics from the Ministry of Higher Education and Science of the Russian Federation (Project FWNF–2022–0006).

PY - 2025/11/13

Y1 - 2025/11/13

N2 - For the Reshetnyak-class homeomorphisms φ:Ω→Y, where Ω 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 (Formula presented.) where 1≤q≤∞, as φ∗u=u∘φ for u∈Lip(Y). We demonstrate the utility of our approach by characterizing the homeomorphisms φ:Ω→Ω′ of domains in some Carnot group G which induce the bounded composition operator (Formula presented.) 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.

AB - For the Reshetnyak-class homeomorphisms φ:Ω→Y, where Ω 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 (Formula presented.) where 1≤q≤∞, as φ∗u=u∘φ for u∈Lip(Y). We demonstrate the utility of our approach by characterizing the homeomorphisms φ:Ω→Ω′ of domains in some Carnot group G which induce the bounded composition operator (Formula presented.) 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.

KW - Carnot group

KW - Composition operator

KW - Distortion of a mapping

KW - Generalized quasiconformal mapping

KW - Metric space

KW - Sobolev class

UR - https://www.scopus.com/pages/publications/105021825645

UR - https://www.mendeley.com/catalogue/ec2609a4-f2f3-3cbd-a8f5-6a151bd9ecf2/

U2 - 10.1007/s13324-025-01142-x

DO - 10.1007/s13324-025-01142-x

M3 - Article

VL - 15

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 6

M1 - 143

ER -