Holomorphic functional calculus of hodge-dirac operators in L^p

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 Axe lsson, Keith, and McIntosh. We obtain a characterization of the property that Π_B has a bounded H^∞ functional calculus, in terms of randomized bounded ness conditions of its resolvent. This allows us to deduce stability under small perturbations of this functional calculus.