The trace problem for Sobolev spaces over the Heisenberg group
type: Item
instance of: scholarly article
title: The trace problem for Sobolev spaces over the Heisenberg group
zbMATH Open document ID: 1152.46023
author: François Vigneron
published in: Journal d'Analyse Mathématique
publication date: 2008-05-27T00:00:00Z
review text: Let \(\mathbb H^d\) be the Heisenberg group. It can be identified with \({\mathbb R}^{2d+1}\) by the exponential coordinates \(x=(p,q,t)\), \(p,q\in {\mathbb R}^d\), \(t\in {\mathbb R}\). The author studies the trace problem for microlocally weighted Hilbertian Sobolev spaces over the Heisenberg group \(\mathbb H^d\) in relation with the canonical sub-Riemannian contact structure \(\varkappa= dt+2(p\, dq- q\, dp)\). The main result of the paper is a complete description of the restriction to hypersurfaces of functions that belong to those Sobolev spaces through a trace and lifting theorem. The function spaces of the restrictions involve an additional weight in the space variable near points where the contact structure of \(\mathbb H^d\) agrees with the hypersurface.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 5279123
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Heisenberg group
zbMATH Keywords: trace problem
zbMATH Keywords: sub-riemannian contact structure
reviewed by: Sergei S. Platonov
MaRDI profile type: Publication
full work available at URL: s11854-008-0009-5
OpenAlex ID: W2021598174
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DOI: 10.1007/S11854-008-0009-5
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description: scientific article; zbMATH DE number 5279123