Factorization of Hardy spaces on local fields
type: Item
instance of: scholarly article
title: Factorization of Hardy spaces on local fields
zbMATH Open document ID: 0632.46047
DOI: 10.1007/BF01456973
author: James E. Daly
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164459
review text: R. Coifman, R. Rochberg, and G. Weiss provided the extension to \(H^ 1\) of several real variables of well-known factorization theorems on the unit disk involving conjugate functions. A. Uchiyama generalized this work to \(H^ p\) on spaces of homogeneous type for a restricted range of p. In this note, these results are extended to \(H^ p\) on a local field for all p and provide an application to commutator operators. The primary result is that if \(f\in H^ p\) and \(1/p=1/q+1/r\), \(0<p,q,r<\infty\), then there exist sequences \((g_ k)\subset H^ q\), \((h_ k)\subset H^ r\) such that \(\| f\| _ p\approx \inf (\sum \| g_ i\| _ q\| h_ i\| _ r)\) where \(f=\sum (h_ iT_{\omega}g_ i-g_ iT'_{\omega}h_ i)\) and where \(T_{\omega}\) is a Calderon-Zygmund singular integral with locally constant kernel \(\omega\).
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4028165
zbMATH Keywords: factorization theorems
zbMATH Keywords: commutator operators
zbMATH Keywords: Calderon-Zygmund singular integral with locally constant kernel
MaRDI profile type: Publication
cites work: Factorization theorems for Hardy spaces in several variables
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Fourier Analysis on Local Fields. (MN-15)
description: scientific article; zbMATH DE number 4028165