Sur les changements de signe d'une fonction harmonique dans le demi-plan
Volume 147 / 2001
Studia Mathematica 147 (2001), 169-182
MSC: 31A05, 31A20.
DOI: 10.4064/sm147-2-5
Abstract
In our recent paper [2], the study of the kernel associated with a singular integral led us to another question, relating to the boundary behaviour of the sign of a harmonic function in a half-plane. In this paper, the possible existence of sign oscillations of the Poisson integral $P(f)$ in the half-plane along rays is related to regularity properties of the boundary function $f$. This allows us to obtain a result of Fatou type for the sign of $P(f)$, under a regularity assumption that we prove to be optimal.
