\(H^ p\)-estimates of holomorphic division formulas
type: Item
instance of: scholarly article
title: \(H^ p\)-estimates of holomorphic division formulas
zbMATH Open document ID: 0857.32006
author: Mats Andersson
author: Hasse Carlsson
published in: Pacific Journal of Mathematics
publication date: 1997-03-12T00:00:00Z
review text: We prove that an explicit formula, due to Berndtsson, for representation of solutions of holomorphic division problems in a strictly pseudoconvex domain admit \(H^p\)-estimates and provides a solution to the following problem: Given bounded holomorphic functions \(G_1, \dots, G_m\) such that \(\sum |G_j |^2 \geq\delta^2\), and \(\varphi \in H^p\), find \(u_j \in H^p\) such that \(\sum G_ju_j = \varphi\). The estimates are based on careful estimates of Hefer functions and a \(T1\)-theorem for Carleson measures, due to Christ and Journé.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32B05
zbMATH DE Number: 940728
zbMATH Keywords: Corona theorem
zbMATH Keywords: division formula
zbMATH Keywords: \(H^ p\)-space
MaRDI profile type: Publication
full work available at URL: pjm.1996.173.307
OpenAlex ID: W1785148575
DOI: 10.2140/PJM.1996.173.307
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description: scientific article; zbMATH DE number 940728