Lusin functions and nontangential maximal functions in the \(H^ p\) theory on the product of upper half-spaces
type: Item
instance of: scholarly article
title: Lusin functions and nontangential maximal functions in the \(H^ p\) theory on the product of upper half-spaces
zbMATH Open document ID: 0567.31003
author: Shuichi Sato
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1985-01-01T00:00:00Z
review text: Let us consider a biharmonic function u, defined on the product space \(D={\mathbb{R}}_+^{n+1}\times {\mathbb{R}}_+^{m+1},\) where \({\mathbb{R}}_+^{n+1}={\mathbb{R}}^ n\times (0,\infty).\) Let A(u) be the Lusin area integral of the biharmonic function u and N(u) its nontangential maximal function. In this paper the author proves the following inequalities: \(\| A(u)\|_ p\leq c_ p \| N(u)\|_ p\) and \(\| N(u)\|_ p\leq c_ p \| A(u)\|_ p,\) where \(c_ p\) is a constant independent of u, \(\| \cdot \|_ p\) is a norm in \(H^ p(D)\) space.
Mathematics Subject Classification ID: 31B30
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 3904945
zbMATH Keywords: \(H^ p\)-space
zbMATH Keywords: biharmonic function
zbMATH Keywords: Lusin area integral
zbMATH Keywords: nontangential maximal function
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228718
OpenAlex ID: W2007566588
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DOI: 10.2748/TMJ/1178228718
description: scientific article; zbMATH DE number 3904945