Anisotropic estimates for sub-elliptic operators

• 来源期刊: 中国科学A辑(英文版)
• 年，卷（期）: 2008,（4）
• 页码范围: 509-522
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-007-0191-4

摘要

In the 1970's,Folland and Stein studied a family of subelliptic scalar operators Lλ which arise naturally in the (-e)b-complex.They introduced weighted Sobolev spaces as the natural spaces for this complex,and then obtained sharp estimates for (-e)b in these spaces using integral kernels and approximate-inverses.In the 1990's,Rumin introduced a differential complex for compact contact manifolds,showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace operator,and derived the necessary estimates for the Laplacian from the Folland Stein analysis.In this paper,we give a self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using integration by parts and a modified approach to bootstrapping.