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

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Chevalier L., Dufresnoy A.

Studia Mathematica

2001

tom 147

nr 2

169-182

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.

Ograniczanie wyników

1 Studia Mathematica

1 Chevalier L.

1 Dufresnoy A.

1 2001

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