Geodesic
Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group
Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 1161-1187

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DOI

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue–Orlicz spaces of a discrete group $\Gamma$ 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 $\Lambda \,\subseteq \,\Gamma$ , the norm of the Hilbert transformand 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.
DOI : 10.4153/CJM-2011-053-9
Mots-clés : 47B49, 43A22, 43A46, 46B28, Fourier multiplier, Toeplitz Schur multiplier, lacunary set, unconditional approximation property, Hilbert transform, Riesz projection 
Neuwirth, Stefan; Ricard, Éric. Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group. Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 1161-1187. doi: 10.4153/CJM-2011-053-9
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     title = {Transfer of {Fourier} {Multipliers} into {Schur} {Multipliers} and {Sumsets} in a {Discrete} {Group}},
     journal = {Canadian journal of mathematics},
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     year = {2011},
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     doi = {10.4153/CJM-2011-053-9},
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