Derivees tangentielles des fonctions de la classe ${\cal A}^{k,\alpha }$ dans les domaines de type fini de ${\Bbb C}^2$
Volume 78 / 2002
Annales Polonici Mathematici 78 (2002), 193-225
MSC: 32A40, 32F18, 32A37.
DOI: 10.4064/ap78-3-1
Abstract
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.
