Let Ω be a domain of finite type in ℂ² and let f be a function holomorphic in Ω and belonging to . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-3-1,
author = {Laurent Verdoucq},
title = {Derivees tangentielles des fonctions de la classe $^{k,$\alpha$}$ dans les domaines de type fini de $\mathbb{C}$$^2$},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {193-225},
zbl = {0998.32003},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-3-1}
}
Laurent Verdoucq. Derivees tangentielles des fonctions de la classe $^{k,α}$ dans les domaines de type fini de ℂ². Annales Polonici Mathematici, Tome 79 (2002) pp. 193-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-3-1/