Holomorphic functional calculus of Hodge-Dirac operators in L p

We study the boundedness of the H (a) 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 I (B) as treated in L (2)(R (n) ; C (N) ) by Axelsson, Keith, and McIntosh. We obtain a characterization of the property that I (B) has a bounded H (a) functional calculus, in terms of randomized boundedness conditions of its resolvent. This allows us to deduce stability under small perturbations of this functional calculus.