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

Volume 147 / 2001

Lucien Chevalier, Alain Dufresnoy Studia Mathematica 147 (2001), 169-182 MSC: 31A05, 31A20. DOI: 10.4064/sm147-2-5

Abstract

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.

Authors

  • Lucien ChevalierInstitut Fourier
    U.M.R. 5582 C.N.R.S./U.J.F.
    B.P. 74
    38402 Saint Martin d'Hères, France
    e-mail
  • Alain DufresnoyInstitut Fourier
    U.M.R. 5582 C.N.R.S./U.J.F.
    B.P. 74
    38402 Saint Martin d'Hères, France
    e-mail

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