Calderón-Zygmund theory for non-integral operators and the functional calculus

  • Sönke Blunck

    Université de Cergy-Pontoise, Cergy-Pontoise, France
  • Peer Christian Kunstmann

    Karlsruher Institut für Technologie (KIT), Germany


We modify Hörmander's well-known weak type (1,1) condition for integral operators (in a weakened version due to Duong and McIntosh) and present a weak type condition for arbitrary operators. Given an operator on with a bounded calculus, we show as an application the -boundedness of the calculus for all , provided the semigroup satisfies suitable weighted -norm estimates with . This generalizes results due to Duong, McIntosh and Robinson for the special case where these weighted norm estimates are equivalent to Poisson-type heat kernel bounds for the semigroup . Their results fail to apply in many situations where our improvement is still applicable, e.g. if is a Schrödinger operator with a singular potential, an elliptic higher order operator with bounded measurable coefficients or an elliptic second order operator with singular lower order terms.

Cite this article

Sönke Blunck, Peer Christian Kunstmann, Calderón-Zygmund theory for non-integral operators and the functional calculus. Rev. Mat. Iberoam. 19 (2003), no. 3, pp. 919–942

DOI 10.4171/RMI/374