A maximal function characterization of a class of Hardy spaces
type: Item
instance of: scholarly article
title: A maximal function characterization of a class of Hardy spaces
zbMATH Open document ID: 0576.42020
author: Robyn Owens
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: An analytic function \(f=u+i\tilde u\) in the upper half plane P belongs to \(H^ p\), \(0<p<\infty\), if and only if \[ \sup_{y>0}\sup_{v\in {\mathbb{R}}^ 1}\frac{1}{\pi}| f(x+iy)|^ p\frac{1}{1+\quad (v- x)^ 2}dx<\infty. \] When u is harmonic in P its maximal function \(u^*\) is defined by \(u^*(t)=\sup \{| u(x+iy)|:| x-t| <y\}\). The author proves necessary and sufficient results in connection with characterizing the \(H^ p\) spaces by the maximal function. The results give an extension of the results of \textit{D. L. Burkholder, R. F. Gundy} and \textit{M. L. Silverstein} [Trans. Am. Math. Soc. 157, 137-153 (1971; Zbl 0223.30048)].
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 3921215
zbMATH Keywords: \(H^ p\) spaces
zbMATH Keywords: maximal function
MaRDI profile type: Publication
full work available at URL: pjm.1985.119.365
OpenAlex ID: W1999676635
DOI: 10.2140/PJM.1985.119.365
description: scientific article; zbMATH DE number 3921215