A \(\varphi\)-transform result for spaces with dominating mixed smoothness properties
type: Item
instance of: scholarly article
title: A \(\varphi\)-transform result for spaces with dominating mixed smoothness properties
zbMATH Open document ID: 0905.46017
DOI: 10.1007/BF03322075
author: Reinhard Hochmuth
published in: Results in Mathematics
publication date: 1998-05-25T00:00:00Z
review text: The main result of this note is a sequence space characterization of certain Banach spaces with dominating mixed smoothness properties, in the spirit of the work of \textit{M. Frazier} and \textit{B. Jawerth} [J. Funct. Anal. 93, No. 1, 34-170 (1990; Zbl 0716.46031)]. More precisely, the author describes the corresponding Triebel-Lizorkin spaces [cf. the book by \textit{H.-J. Schmeisser} and \textit{H. Triebel}: ``Topics in Fourier analysis and function spaces'' (1987; Zbl 0661.46024) for details on these spaces] in terms of appropriate Fourier decompositions and derives therefrom the fact that these spaces are retracts of certain solid sequence spaces, for the full range of parameters, i.e., indices \(p,q\) down to \(0\). Although the general approach follows the lines of previous work the details are technically quite involved.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 46F99
zbMATH DE Number: 1140111
zbMATH Keywords: product-convolution operator
zbMATH Keywords: Schatten class
zbMATH Keywords: Wiener amalgam spaces on groups
zbMATH Keywords: metaplectic representation
zbMATH Keywords: Banach spaces with dominating mixed smoothness properties
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: Fourier decompositions
reviewed by: H. G. Feichtinger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1140111