Densité de l'intégrale d'aire et intégrales singulières

Lucien Chevalier Institut Fourier, U.M.R. 5582 C.N.R.S./U.J.F. Alain Dufresnoy Institut Fourier, U.M.R. 5582 C.N.R.S./U.J.F.

TBD mathscidoc:1701.332939

Arkiv for Matematik, 38, (2), 209-221, 1998.10
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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@inproceedings{lucien1998densité,
  title={Densité de l'intégrale d'aire et intégrales singulières},
  author={Lucien Chevalier, and Alain Dufresnoy},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203559078109748},
  booktitle={Arkiv for Matematik},
  volume={38},
  number={2},
  pages={209-221},
  year={1998},
}
Lucien Chevalier, and Alain Dufresnoy. Densité de l'intégrale d'aire et intégrales singulières. 1998. Vol. 38. In Arkiv for Matematik. pp.209-221. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203559078109748.
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