Derivees tangentielles des fonctions de la classe ${\cal A}^{k,\alpha }$ dans les domaines de type fini de ${\Bbb C}^2$

Tom 78 / 2002

Laurent Verdoucq Annales Polonici Mathematici 78 (2002), 193-225 MSC: 32A40, 32F18, 32A37. DOI: 10.4064/ap78-3-1


Let ${\mit \Omega }$ be a domain of finite type in ${\mathbb C}^2$ and let $f$ be a function holomorphic in ${\mit \Omega }$ and belonging to ${\cal C}^{k,\alpha } ( \overline {{\mit \Omega }})$. 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 $\partial {\mit \Omega }$. 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.


  • Laurent VerdoucqCNRS–URA 751, Bât. M2, Mathématiques
    Université des Sciences et Technologies de Lille
    59655 Villeneuve d'Ascq Cedex, France

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