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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-5,
author = {Lucien Chevalier and Alain Dufresnoy},
title = {Sur les changements de signe d'une fonction harmonique dans le demi-plan},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {169-182},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-5}
}
Lucien Chevalier; Alain Dufresnoy. Sur les changements de signe d'une fonction harmonique dans le demi-plan. Studia Mathematica, Tome 147 (2001) pp. 169-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-5/