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

• Autorzy: Laurent Verdoucq
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32A40: Boundary behavior of holomorphic functions
• 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
• 32F18: Finite-type conditions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 3
• Strony: 193-225

Daty

wydano

2002

Twórcy

autor

Laurent Verdoucq

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

Identyfikatory

DOI

10.4064/ap78-3-1