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

Stefan Neuwirth (1) , Éric Ricard (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Mots clés: Fourier multiplier; Toeplitz Schur multiplier; lacunary set; unconditional approximation property; Hilbert transform; Riesz projection

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Stefan Neuwirth, Éric Ricard. Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group. Canadian Journal of Mathematics, 2011, 63 (5), pp.1161-1187. ⟨10.4153/CJM-2011-053-9⟩. ⟨hal-00451399v2⟩