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

Laurent Verdoucq¹

¹ CNRS–URA 751, Bât. M2, Mathématiques Université des Sciences et Technologies de Lille 59655 Villeneuve d'Ascq Cedex, France

Annales Polonici Mathematici, Tome 78 (2002) no. 3, pp. 193-225.

Résumé

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.

Détail

DOI : 10.4064/ap78-3-1

Mots-clés : mit omega domain finite type mathbb function holomorphic mit omega belonging cal alpha overline mit omega prove existence boundary values suitable derivatives order greater gain derivatives holds complex tangential direction precisely related geometry partial mit omega prove property non isotropic lder regularity these boundary values generalizes results given bruna ortega unit ball