A connection between Fourier and Schur multipliers
type: Item
instance of: scholarly article
title: A connection between Fourier and Schur multipliers
zbMATH Open document ID: 0863.42011
DOI: 10.1007/BF01203030
author: Victor Olevskii
published in: Integral Equations and Operator Theory
publication date: 1997-05-27T00:00:00Z
review text: Let \(S_p\) denote the Schatten classes of compact operators in \(L_2(\mathbb{T})\). The author constructs a continuous function \(f: \mathbb{T}\to\mathbb{C}\) such that \(f\) is a Fourier multiplier in \(\ell_p\), \(1<p<\infty\), but \(\varphi(x,y)=f(x-y)\) is not a Schur multiplier in \(S_p\), \(p\neq 2\).
Mathematics Subject Classification ID: 42A45
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B49
zbMATH DE Number: 935123
zbMATH Keywords: Schatten classes
zbMATH Keywords: Fourier multiplier
zbMATH Keywords: Schur multiplier
MaRDI profile type: Publication
cites work: Q5833361
cites work: Q4112997
cites work: Q3497208
cites work: An estimate for Schur multipliers in \(S_ p\)-classes
cites work: Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
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description: scientific article; zbMATH DE number 935123