Sur les changements de signe d'une fonction harmonique dans le demi-plan

Lucien Chevalier, Alain Dufresnoy
2001 Studia Mathematica  
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.
doi:10.4064/sm147-2-5 fatcat:ykzft3dq75fudn2zk5t7rougpy