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Derivees tangentielles des fonctions de la classe $𝓐^{k,α}$ dans les domaines de type fini de ℂ²

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Verdoucq L.

Annales Polonici Mathematici

2002

tom 78

nr 3

193-225

Let Ω be a domain of finite type in ℂ² and let f be a function holomorphic in Ω and belonging to $𝓒^{k,α}(Ω̅ )$. We prove the existence of boundary values for some suitable derivatives of f of order greater than k. The gain of derivatives holds in the complex-tangential direction and it is precisely related to the geometry of ∂Ω. Then we prove a property of non-isotropic Hölder regularity for these boundary values. This generalizes some results given by J. Bruna and J. M. Ortega for the unit ball.

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1 Annales Polonici Mathematici

1 Verdoucq L.

1 2002

Wyniki wyszukiwania

Derivees tangentielles des fonctions de la classe $𝓐^{k,α}$ dans les domaines de type fini de ℂ²