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

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 1, page 251-292
- ISSN: 0214-1493

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topGrellier, Sandrine. "Behavior of holomorphic functions in complex tangential directions in a domain of finite type in Cn.." Publicacions Matemàtiques 36.1 (1992): 251-292. <http://eudml.org/doc/41152>.

@article{Grellier1992,

abstract = {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.},

author = {Grellier, Sandrine},

journal = {Publicacions Matemàtiques},

keywords = {Funciones holomorfas; Funciones de variable compleja; Dominios convexos; domain of finite type; complex tangential directions; holomorphic function},

language = {eng},

number = {1},

pages = {251-292},

title = {Behavior of holomorphic functions in complex tangential directions in a domain of finite type in Cn.},

url = {http://eudml.org/doc/41152},

volume = {36},

year = {1992},

}

TY - JOUR

AU - Grellier, Sandrine

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

JO - Publicacions Matemàtiques

PY - 1992

VL - 36

IS - 1

SP - 251

EP - 292

AB - 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.

LA - eng

KW - Funciones holomorfas; Funciones de variable compleja; Dominios convexos; domain of finite type; complex tangential directions; holomorphic function

UR - http://eudml.org/doc/41152

ER -

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