Comparaison des projecteurs de Bergman et Szegö et applications. (Comparison of the Bergman and Szegö projectors, and applications)
type: Item
instance of: scholarly article
title: Comparaison des projecteurs de Bergman et Szegö et applications. (Comparison of the Bergman and Szegö projectors, and applications)
zbMATH Open document ID: 0699.32003
DOI: 10.1007/BF02387365
published in: Arkiv för Matematik
publication date: 1990-01-01T00:00:00Z
review text: Denote by B and S the Bergman and Szegö projections, respectively, associated to a bounded domain D in \({\mathbb{C}}^ n\). When comparing solutions to the \({\bar \partial}\)-equation minimizing \({\mathcal L}^ 2\)- norms over bD and over D, respectively, one is led to compare S-B. In the paper under review, the author considers strictly pseudoconvex domains and gives \({\mathcal L}^ p\)-type estimates \((1<p)\) for Su-Bu in terms of \({\bar \partial}u\). The method is to use the known asymptotic expansions of S and B, and to exhibit the principal part of S-B as an explicit integral operator. An application to \({\mathcal L}^ p(bD)\)-estimates for the canonical solution u-Bu to \({\bar \partial}u=f\) is also given.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4146386
zbMATH Keywords: Bergman projection
zbMATH Keywords: Szegö projection
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: strictly pseudoconvex domains
author: A. Cumenge
reviewed by: Emil J. Straube
MaRDI profile type: Publication
cites work: Mesures de Carleson d'ordre $\alpha$ et solutions au bord de l'équation $\overline\partial$
cites work: Henkin-Ramirez kernels with weight factors
cites work: Q3762839
cites work: Extension dans des classes de Hardy de fonctions holomorphes et estimations de type ''Mesures de Carleson'' pour l'équation \(\bar\partial\)
cites work: ZEROS OF HOLOMORPHIC FUNCTIONS OF FINITE ORDER AND WEIGHTED ESTIMATES FOR SOLUTIONS OF THE $\bar\partial$-EQUATION
cites work: INTEGRAL REPRESENTATION OF FUNCTIONS IN STRICTLY PSEUDOCONVEX DOMAINS AND APPLICATIONS TO THE $ \overline{\partial}$-PROBLEM
cites work: Q4001795
cites work: The Szegö kernel in terms of Cauchy-Fantappie kernels
cites work: The Hölder continuity of the Bergman projection and proper holomorphic mappings
cites work: Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
cites work: Valeurs au bord pour les solutions de l'opérateur $d^n$, et caractérisation des zéros des fonctions de la classe de Nevanlinna
cites work: Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
Recommended article: Comparing the Bergman and the Szegö projections
Recommended article: Comparison of the Bergman and Szegö kernels
Recommended article: A direct connection between the Bergman and Szegő projections
Recommended article: Comparing the Bergman and Szegö projections on domains with subelliptic boundary Laplacian
Recommended article: Q3324232
Recommended article: Szegö and Bergman projections on non-smooth planar domains
Recommended article: Q4378394
Recommended article: A general description of the Bergman projection
Recommended article: Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$
Recommended article: Q4878744
description: scientific article; zbMATH DE number 4146386