Behavior of holomorphic functions in complex tangential directions in a domain of finite type in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Behavior of holomorphic functions in complex tangential directions in a domain of finite type in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0758.32004
DOI: 10.5565/PUBLMAT_36192_20
author: Sandrine Grellier
published in: Publicacions Matemàtiques
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/41152
review text: The author compares the behavior of holomorphic functions in complex tangential directions and all directions. He shows that if \(\Omega\) is a domain of finite type in \(\mathbb{C}^ n\) then the regularity in complex tangential directions of a holomorphic function in \(\Omega\) implies the regularity in all directions. He gives a pointwise inequality in both directions between the gradients and the complex tangential gradients. He also characterizes Besov, Sobolev and Lipschitz spaces of holomorphic functions by the behavior of complex tangential derivations.
Mathematics Subject Classification ID: 32A40
zbMATH DE Number: 94221
zbMATH Keywords: domain of finite type
zbMATH Keywords: complex tangential directions
zbMATH Keywords: holomorphic function
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
OpenAlex ID: W2150122827
description: scientific article; zbMATH DE number 94221