Holomorphic functional calculus of Hodge-Dirac operators in Lp

2009/07/14 by Tuomas Hytönen, Tuomas Hytonen, Hytonen, Tuomas +4
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.AP #math.FA #msc:47A60 #msc:47F05

paper · pdf · doi:10.48550/arxiv.0907.2274

25 pages, submitted

arxiv created 2009/07/14 · arxiv updated 2009/12/01

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.

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