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arXiv · 1001.5332

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

Stefan Neuwirth·Éric Ricard
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Abstract

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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BibTeXRIS

Stefan Neuwirth, Éric Ricard. 2012-06-23. Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group. https://doi.org/10.4153/cjm-2011-053-9

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