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Densité de l'intégrale d'aire et intégrales singulières
- Source :
- Ark. Mat. 38, no. 2 (2000), 209-221
- Publication Year :
- 2000
- Publisher :
- Institut Mittag-Leffler, 2000.
-
Abstract
- 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.
Details
- Language :
- French
- Database :
- OpenAIRE
- Journal :
- Ark. Mat. 38, no. 2 (2000), 209-221
- Accession number :
- edsair.doi.dedup.....87d5d1b59c29e580971d55e53ec6eab1