Quadratic estimates and functional calculi of perturbed Dirac operators

• 成果类型: Article
• 署名作者: Axelsson, A; Keith, S; McIntosh, A
• 署名单位: Australian National University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0464-x
• 发表日期: 2006
• 页码: 455-497
• 关键词: square-root problem; elliptic-operators; kato problem; INTEGRALS

摘要

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge-Dirac operator on compact manifolds depend analytically on L-infinity changes in the metric. We also recover a unified proof of many results in the Calderon program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.