 |
|
Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group |
Canad. J. Math. 63(2011), 1161-1187
Published:2011-08-03
Printed: Oct 2011
Printed: Oct 2011
- Stefan Neuwirth,
- Éric Ricard,
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 |
| MSC Classifications: |
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] |