Hardy spaces on some pseudoconvex domains
type: Item
instance of: scholarly article
title: Hardy spaces on some pseudoconvex domains
zbMATH Open document ID: 0802.32012
DOI: 10.1007/BF02921583
author: Galia Dafni
published in: The Journal of Geometric Analysis
publication date: 1994-11-01T00:00:00Z
review text: We consider Hardy spaces \({\mathcal H}^ p\), \(p\leq 1\), of holomorphic functions in the interior of \(\Omega\), where \(\Omega\) is either a strongly pseudoconvex domain in \(\mathbb{C}^ n\) or a weakly pseudoconvex domain of finite type in \(\mathbb{C}^ 2\). We exhibit an atomic decomposition for the boundary values of these functions (in the sense of distributions), thus showing they belong to the local real Hardy spaces \({\mathcal H}^ p(\partial\Omega)\).
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 653340
zbMATH Keywords: \(H^ p\)-spaces
zbMATH Keywords: pseudoconvex domains
zbMATH Keywords: atomic decomposition
MaRDI profile type: Publication
cites work: The Hull of Holomorphy of a Nonisotropic Ball in a Real Hypersurface of Finite Type
cites work: An atomic decomposition of distributions in parabolic \(H^p\) spaces
cites work: Estimates of invariant metrics on pseudoconvex domains of dimension two
cites work: Q2548398
cites work: Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation. (Calderón-Zygmund operators, para-accretive functions and interpolation)
cites work: Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
cites work: Q3700300
cites work: The atomic decomposition for Hardy spaces in several complex variables
cites work: A local version of real Hardy spaces
cites work: A note on Hardy spaces and functions of bounded mean oscillation on domains in \(\mathbb{C}^ n\)
cites work: On decomposition theorems for Hardy spaces on domains in \(\mathbb{C}^ n\) and applications
cites work: A decomposition into atoms of distributions on spaces of homogeneous type
cites work: Boundary behavior of the Bergman kernel function in \({\mathbb{C}}^ 2\)
cites work: Boundary behavior of functions holomorphic in domains of finite type
cites work: Balls and metrics defined by vector fields. I: Basic properties
cites work: Estimates for the Bergman and Szegö kernels in \({\mathbb{C}}^ 2\)
cites work: Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
cites work: On the atomic decomposition for Hardy spaces
description: scientific article; zbMATH DE number 653340