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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive
Sibirsk. Mat. Zh., 2014 Volume 55, Number 5, Pages 1001–1039 (Mi smj2586)
This article is cited in 17 papers

Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings

S. K. Vodop'yanovab, N. A. Evseevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the properties of the mappings on a Carnot group which induce, via the change-of-variables rule, the isomorphisms of Sobolev spaces with the summability exponent different from the Hausdorff dimension of the group.

Keywords: superposition operator, Sobolev space, quasi-isometry, Carnot group.

UDC: 517.518+517.54

Received: 20.12.2013


 English version: Siberian Mathematical Journal, 2014, 55:5, 817–848

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© Steklov Math. Inst. of RAS, 2024