Behavior of holomorphic functions in complex tangential directions in a domain of finite type in Cn.

Título inglés Behavior of holomorphic functions in complex tangential directions in a domain of finite type in Cn.
Título español Comportamiento de funciones holomorfas en direcciones tangenciales complejas en un dominio de tipo finito en Cn.
Autor/es Grellier, Sandrine
Organización Dép. Math. Inform. Univ. Orléans, Orléans, Francia
Revista 0214-1493
Publicación 1992, 36 (1): 251-292, 25 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let Ω be a domain in Cn. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential directions implies the corresponding regularity in all directions. We give a pointwise inequality in both directions between the gradients and the complex tangential gradients. We characterize Besov, Sobolev and Lipschitz spaces of holomorphic functions defined on Ω by the behavior of complex tangential derivatives.
Clasificación UNESCO 120211
Palabras clave español Funciones holomorfas ; Funciones de variable compleja ; Dominios convexos
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