Fourier multipliers for Besicovitch spaces
type: Item
instance of: scholarly article
title: Fourier multipliers for Besicovitch spaces
zbMATH Open document ID: 0927.42003
DOI: 10.4171/ZAA/859
author: K. Appert
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-12-13T00:00:00Z
review text: The notion of Fourier multiplier \(M\) for the space \(L^q(\mathbb{R}^s)\), where \(1<q<\infty\), is extended to the case of a Fourier multiplier \(\widetilde M\) for the space \(B^q_{\text{ap}}(\mathbb{R}^s,\Lambda)\) of Besicovitch almost periodic functions with spectrum \(\Lambda\), where \(\widetilde M= (M(\lambda))_{\lambda\in \Lambda}\), where the functions from \(B^q_{\text{ap}}(\mathbb{R}^s,\Lambda)\) are treated as tempered distributions. There are also defined Sobolev-Besicovitch spaces \(H^{m,q}_{\text{ap}}(\mathbb{R}^s,\Lambda)\) of order \(m\) and type \(H\) and Sobolev-Besicovitch spaces \(W^{m,q}_{\text{ap}}(\mathbb{R}^s,\Lambda)\) of order \(m\) and type \(W\), where \(1<q<\infty\) and \(m\in\mathbb{R}\) in the first case, \(m\in\mathbb{N}\) in the second one. If \(1<q<\infty\) and \(N\in\mathbb{N}\), \(N\geq 1\), there is proved the identity \(H^{N,q}_{\text{ap}}(\mathbb{R}^s, \Lambda)= W^{N,q}_{\text{ap}}(\mathbb{R}^s, \Lambda)\).
Mathematics Subject Classification ID: 42A75
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 1270170
zbMATH Keywords: multipliers
zbMATH Keywords: Besicovitch almost periodic functions
zbMATH Keywords: tempered distributions
zbMATH Keywords: Sobolev-Besicovitch spaces
reviewed by: Julian Musielak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1270170