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

• Autorzy: Lucien Chevalier , Alain Dufresnoy
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 31A05: Harmonic, subharmonic, superharmonic functions
• 31A20: Boundary behavior (theorems of Fatou type, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 2
• Strony: 169-182

Daty

wydano

2001

Twórcy

autor

Lucien Chevalier

• Institut Fourier, U.M.R. 5582 C.N.R.S./U.J.F., B.P. 74, 38402 Saint Martin d'Hères, France

autor

Alain Dufresnoy

• Institut Fourier, U.M.R. 5582 C.N.R.S./U.J.F., B.P. 74, 38402 Saint Martin d'Hères, France

Identyfikatory

DOI

10.4064/sm147-2-5