On the Hardy space \(H^ 1\) on product of half-spaces
type: Item
instance of: scholarly article
title: On the Hardy space \(H^ 1\) on product of half-spaces
zbMATH Open document ID: 0633.30030
author: Nativi Viana Pereiro Bertolo
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: We show that the Hardy space \(H^ 1_{anal}({\mathbb{R}}^ 2_ +\times {\mathbb{R}}^ 2_ +)\) can be identified with the class of functions f such that f and all its double and partial Hilbert transforms \(H_ kf\) belong to \(L^ 1({\mathbb{R}}^ 2)\). A basic tool used in the proof is the bi- subharmonicity of \(| F| ^ q\), where F is a vector that satisfies a generalized conjugate system of Cauchy-Riemann type.
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 31A05
zbMATH DE Number: 4029911
zbMATH Keywords: system of Cauchy-Riemann type
zbMATH Keywords: \(H^ 1\)-spaces
zbMATH Keywords: biharmonic functions
MaRDI profile type: Publication
full work available at URL: pjm.1989.138.347
OpenAlex ID: W2010578054
DOI: 10.2140/PJM.1989.138.347
description: scientific article; zbMATH DE number 4029911