Holomorphic functional calculus of Hodge-Dirac operators in Lp

2009/07/14 by Tuomas Hytönen, Hytonen, Tuomas, Alan McIntosh +3
Mathematics · #Advanced Harmonic Analysis Research #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0907.2274

Abstract

We study the boundedness of the H^∞ functional calculus for differential operators acting in (L^p(ℝⁿ;ℂ^N)). For constant coefficients, we give simple conditions on the symbols implying such boundedness. For non-constant coefficients, we extend our recent results for the (L^p) theory of the Kato square root problem to the more general framework of Hodge-Dirac operators with variable coefficients (Π_B) as treated in (L²(ℝⁿ;ℂ^N)) by Axelsson, Keith, and McIntosh. We obtain a characterization of the property that (Π_B) has a bounded (H^∞) functional calculus, in terms of randomized boundedness conditions of its resolvent. This allows us to deduce stability under small perturbations of this functional calculus.

Related

• Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L^p
• L^p-Analysis of the Hodge--Dirac operator associated with Witten\n Laplacians on complete Riemannian manifolds
• Hodge-Dirac, Hodge-Laplacian and Hodge-Stokes operators in L^p spaces on Lipschitz domains
• Stability in p of the H-infinity calculus of first-order systems in L^p
• L^p-L^q theory for holomorphic functions of perturbed first order Dirac operators