Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings

DOI10.1134/S1064562415050117zbMath1348.46044OpenAlexW2292412789MaRDI QIDQ906087

Nikita Evseev, Sergei Vodop'yanov

Publication date: 29 January 2016

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562415050117

zbMATH Keywords

Sobolev spacequasi-isometricCarnot groupquasi-conformal

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Implicit function theorems, Jacobians, transformations with several variables (26B10)

Related Items (5)

Bounded composition operator on Lorentz spaces ⋮ Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds ⋮ Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings ⋮ The composition operator on mixed-norm Lebesgue spaces ⋮ Composition operators in weighted Sobolev spaces on the Carnot group

Cites Work

• Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
• Forme abstraite du théorème de capacitabilité
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings
• Quasiconformal mappings and spaces of functions with generalized first derivatives
• Criteria for the removability of sets in spaces of \(L^1_p\) quasiconformal and quasi-isometric mappings
• Monotone functions and quasiconformal mappings on Carnot groups
• Differentiability of curves in the category of Carnot manifolds
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