Bergman and Hardy spaces on model domains
type: Item
instance of: scholarly article
title: Bergman and Hardy spaces on model domains
zbMATH Open document ID: 0909.32001
author: Fritz Haslinger
published in: Illinois Journal of Mathematics
publication date: 1998-08-20T00:00:00Z
review text: In the first part of this paper we show that each function which belongs to the \(L^2\)-space of the boundary of a model domain and which is also a CR-distribution can be extended to a function holomorphic on the whole domain which belongs to the corresponding Hardy space \(H^2\). The extension is expressed in terms of a corresponding entire function with a growth condition depending on the shape of the model domain. In the following parts we consider Bergman and Szegő kernels on model domains and apply these results to determine the boundary limits of the Bergman kernel on the diagonal of a bounded pseudoconvex domain in \(\mathbb{C}^{n+1}\), that is \(h\)-extendible at a boundary point \(P\), using a reduction to the model case due to Boas, Straube and Yu.
reviewed by: Fritz Haslinger
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 30D20
Mathematics Subject Classification ID: 32V05
zbMATH DE Number: 1193074
zbMATH Keywords: Hardy space \(H^2\)
zbMATH Keywords: CR-distribution
zbMATH Keywords: entire function
zbMATH Keywords: Szegő kernels
zbMATH Keywords: boundary limits
zbMATH Keywords: Bergman kernel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1193074