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Quadratic estimates and functional calculi of perturbed Dirac operators

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Abstract

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 ∞ changes in the metric. We also recover a unified proof of many results in the Calderón program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.

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  1. Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia

    Andreas Axelsson, Stephen Keith & Alan McIntosh

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  1. Andreas Axelsson
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  2. Stephen Keith
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  3. Alan McIntosh
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Correspondence to Andreas Axelsson, Stephen Keith or Alan McIntosh.

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Axelsson, A., Keith, S. & McIntosh, A. Quadratic estimates and functional calculi of perturbed Dirac operators. Invent. math. 163, 455–497 (2006). https://doi.org/10.1007/s00222-005-0464-x

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