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

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

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.

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Veröffentlicht in:Siberian mathematical journal 2014-09, Vol.55 (5), p.817-848
Hauptverfasser: Vodop’yanov, S. K., Evseev, N. A.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446614050048