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.
Mots-clés :
recent paper study kernel associated singular integral led another question relating boundary behaviour sign harmonic function half plane paper possible existence sign oscillations poisson integral half plane along rays related regularity properties boundary function allows obtain result fatou type sign under regularity assumption prove optimal
Affiliations des auteurs :
Lucien Chevalier
1
;
Alain Dufresnoy
1
1
Institut Fourier U.M.R. 5582 C.N.R.S./U.J.F. B.P. 74 38402 Saint Martin d'Hères, France
@article{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},
pages = {169--182},
year = {2001},
volume = {147},
number = {2},
doi = {10.4064/sm147-2-5},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm147-2-5/}
}
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AU - Lucien Chevalier
AU - Alain Dufresnoy
TI - Sur les changements de signe
d'une fonction harmonique dans le demi-plan
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Lucien Chevalier; Alain Dufresnoy. Sur les changements de signe
d'une fonction harmonique dans le demi-plan. Studia Mathematica, Tome 147 (2001) no. 2, pp. 169-182. doi: 10.4064/sm147-2-5
