Arkiv för Matematik

  • Ark. Mat.
  • Volume 38, Number 2 (2000), 209-221.

Densité de l'intégrale d'aire et intégrales singulières

Lucien Chevalier and Alain Dufresnoy

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In his 1983 paper [3], R. F. Gundy introduced a new functional related to the Littlewood-Paley theory, called the density of the area integral. In this paper, we prove that this functional (although highly non-linear) can be expressed as the principal value of an explicit singular integral. This result provides us with a new and precise connection between the density of the area integral and the theory of Calderón-Zygmund operators. It does not seem to be a consequence of the standard Calderón-Zygmund-Cotlar theory, because the sign of a harmonic function in the half-space fails to have, in some appropriate sense, boundary limits.

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Ark. Mat., Volume 38, Number 2 (2000), 209-221.

Received: 12 October 1998
Revised: 12 January 1999
First available in Project Euclid: 31 January 2017

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2000 © Institut Mittag-Leffler


Chevalier, Lucien; Dufresnoy, Alain. Densité de l'intégrale d'aire et intégrales singulières. Ark. Mat. 38 (2000), no. 2, 209--221. doi:10.1007/BF02384317.

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  • Meyer, Y., Opérateurs de Calderón-Zygmund, Hermann, Paris, 1990.