On Hardy-Bessel potential spaces over the ring of integers in a local field
type: Item
instance of: scholarly article
title: On Hardy-Bessel potential spaces over the ring of integers in a local field
zbMATH Open document ID: 0819.43001
DOI: 10.1007/BF01908644
author: Jun Tateoka
published in: Analysis Mathematica
publication date: 1995-08-22T00:00:00Z
review text: The Hardy-Bessel potential space \(F^ \alpha_ p\) is defined as the class of distributions \(f\) such that \(g_ \alpha \in L^ p\) with the Littlewood-Paley type function \(g_ \alpha\). Then the author gives two equivalent quasi-norms on \(F^ \alpha_ p\) by the Bessel potential \(J^ \alpha\) and the area function \(S^ \alpha_ r\). The topic of this note is very interesting, not only because the technique used for a local field is quite different from that for \(\mathbb{R}^ n\), but also because the topic on a local field has importance for some applications.
Mathematics Subject Classification ID: 43A17
Mathematics Subject Classification ID: 43A70
Mathematics Subject Classification ID: 11S85
zbMATH DE Number: 598217
zbMATH Keywords: Hardy-Bessel potential spaces
zbMATH Keywords: quasi-norms
zbMATH Keywords: local fields
reviewed by: Su Weiyi
MaRDI profile type: Publication
cites work: Q4201053
cites work: Q3997391
cites work: Q5522602
cites work: Fourier Analysis on Local Fields. (MN-15)
full work available at URL: https://doi.org/10.1007/bf01908644
OpenAlex ID: W34494112
description: scientific article; zbMATH DE number 598217