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Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group

Published online by Cambridge University Press:  20 November 2018

Stefan Neuwirth  and
Éric Ricard
Stefan Neuwirth
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 25000 Besançon, France email: stefan.neuwirth@univ-fcomte.freric.ricard@univ-fcomte.fr
Éric Ricard
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 25000 Besançon, France email: stefan.neuwirth@univ-fcomte.freric.ricard@univ-fcomte.fr
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Abstract

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We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue–Orlicz spaces of a discrete group $\Gamma$ and relative Toeplitz-Schur multipliers on Schatten–von-Neumann–Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum $\Lambda \,\subseteq \,\Gamma$, the norm of the Hilbert transformand the Riesz projection on Schatten–von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten–von-Neumann classes with exponent less than 1.

Keywords

47B4943A2243A4646B28Fourier multiplierToeplitz Schur multiplierlacunary setunconditional approximation propertyHilbert transformRiesz projection
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 5 , 18 October 2011 , pp. 1161 - 1187
Copyright
Copyright © Canadian Mathematical Society 2011

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