CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

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

  Published:2011-08-03
 Printed: Oct 2011
  • Stefan Neuwirth,
    Laboratoire de Mathématiques, Université de Franche-Comté, 25000 Besançon, France
  • Éric Ricard,
    Laboratoire de Mathématiques, Université de Franche-Comté, 25000 Besançon, France
Format:   LaTeX   MathJax   PDF  

Abstract

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group $\varGamma$ 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 $\varLambda\subseteq\varGamma$, the norm of the Hilbert transform and 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: Fourier multiplier, Toeplitz Schur multiplier, lacunary set, unconditional approximation property, Hilbert transform, Riesz projection Fourier multiplier, Toeplitz Schur multiplier, lacunary set, unconditional approximation property, Hilbert transform, Riesz projection
MSC Classifications: 47B49, 43A22, 43A46, 46B28 show english descriptions Transformers, preservers (operators on spaces of operators)
Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
47B49 - Transformers, preservers (operators on spaces of operators)
43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/