Holomorphic functional calculus of Hodge-Dirac operators in L p

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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Correspondence to Pierre Portal.

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Hytönen, T., McIntosh, A. & Portal, P. Holomorphic functional calculus of Hodge-Dirac operators in L p . J. Evol. Equ. 11, 71–105 (2011). https://doi.org/10.1007/s00028-010-0082-y

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Mathematics Subject Classification (2010)

  • 42B37
  • 47A60
  • 47F05