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1. CJM 2011 (vol 63 pp. 1161)
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Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group 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 Categories:47B49, 43A22, 43A46, 46B28 |