Abstract
We study the boundedness of the H ∞ functional calculus for differential operators acting in L p (R n ; 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 L 2(R n ; 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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