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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.
Lucien Chevalier, and Alain Dufresnoy. "Sur les changements de signe d'une fonction harmonique dans le demi-plan." Studia Mathematica 147.2 (2001): 169-182. <http://eudml.org/doc/284542>.
@article{LucienChevalier2001, author = {Lucien Chevalier, Alain Dufresnoy}, journal = {Studia Mathematica}, language = {fre}, number = {2}, pages = {169-182}, title = {Sur les changements de signe d'une fonction harmonique dans le demi-plan}, url = {http://eudml.org/doc/284542}, volume = {147}, year = {2001}, }
TY - JOUR AU - Lucien Chevalier AU - Alain Dufresnoy TI - Sur les changements de signe d'une fonction harmonique dans le demi-plan JO - Studia Mathematica PY - 2001 VL - 147 IS - 2 SP - 169 EP - 182 LA - fre UR - http://eudml.org/doc/284542 ER -