Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group

Details Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group

2010-01-29

arxiv.org/abs/1001.5332v1

Mathematics

Functional Analysis

Scientific paper

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group 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, that is, by a subset of the group; the norm of the Hilbert transform and the Riesz projection on Schatten-von-Neumann classes with exponent a power of 2; the norm of Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less than 1.

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