Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group

Neuwirth, Stefan ; Ricard, Éric

Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 1161-1187

Résumé

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.

Détail

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

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