1. Densité de l'intégrale d'aire et intégrales singulières
- Author
-
Lucien Chevalier and Alain Dufresnoy
- Subjects
Harmonic function ,General Mathematics ,Principal value ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,Boundary (topology) ,Singular integral ,Connection (mathematics) ,Mathematics - 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.
- Published
- 2000