Anisotropic estimates for sub-elliptic operators
type: Item
instance of: scholarly article
title: Anisotropic estimates for sub-elliptic operators
zbMATH Open document ID: 1166.35010
published in: Science in China. Series A
publication date: 2008-09-09T00:00:00Z
review text: In the 1970's Folland and Stein investigated a family os subelliptic scalar operators \(\mathcal{L}_\lambda\), arising naturally in the \(\overline{\partial}_b\)-complex. They introduced weighted Sobolev spaces as the natural spaces to deal with this complex, and then they obtained sharp estimates for \(\overline{\partial}_b\) in these spaces using integral kernels and approximate inverse. In the 1990's Rumin introduced a differential complex for compact contact manifolds showing that Folland-Stein operators play a central role in the analysis of the corresponding Laplacian and studied the estimates on the Laplacian using Folland-Stein analysis. In this paper the authors give a self-contained proof of sharp estimates in Folland-Stein spaces for the operators studied by Rumin; the essential tools in the proof are integration by parts and a modified bootstrapping method.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 32V20
zbMATH DE Number: 5323336
zbMATH Keywords: anisotropic Sobolev spaces
zbMATH Keywords: contact manifolds
zbMATH Keywords: Folland-Stein operators
zbMATH Keywords: Folland-Stein spaces
author: John S. Bland
author: Thomas E. Duchamp
MaRDI profile type: Publication
full work available at URL: s11425-007-0191-4
OpenAlex ID: W2140675979
cites work: Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
cites work: Differential forms on contact manifolds
DOI: 10.1007/S11425-007-0191-4
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description: scientific article; zbMATH DE number 5323336