Besov spaces and Herz spaces on local fields
type: Item
instance of: scholarly article
title: Besov spaces and Herz spaces on local fields
zbMATH Open document ID: 0931.42014
DOI: 10.1007/BF02871839
author: Weixing Zheng
author: Yueping Zhu
published in: Science in China. Series A
publication date: 2000-02-14T00:00:00Z
review text: Let \(K\) be a local field and \(K^n\) an \(n\)-dimensional vector space over \(K\). The authors first establish a theorem on the relationship between the Besov spaces and the Herz spaces over \(K^n\) via the Fourier transform. Then they give a multiplier theorem on the Hardy spaces \(H^p(K^n)\) for \(0<p<1\) by means of the Herz spaces. Moreover, they establish the atomic decompositions of the weighted Besov spaces over \(K^n\).
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A22
zbMATH DE Number: 1281449
zbMATH Keywords: local field
zbMATH Keywords: Besov space
zbMATH Keywords: Herz space
zbMATH Keywords: multiplier
zbMATH Keywords: atom
zbMATH Keywords: weight
zbMATH Keywords: Hardy space
reviewed by: Dachun Yang
MaRDI profile type: Publication
cites work: Fourier Analysis on Local Fields. (MN-15)
cites work: Embedding and multiplier theorems for 𝐻^{𝑃}(𝑅ⁿ)
cites work: The decomposition of weighted Herz space on \(\mathbb{R}^ n\) and its applications
cites work: The weighted Herz-type Hardy space and its applications
cites work: Homogeneous Besov spaces on locally compact Vilenkin groups
cites work: Q3816466
cites work: The decomposition of Herz spaces on local fields and its applications
description: scientific article; zbMATH DE number 1281449