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

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.

arXiv commentCorresponds to the version published in the Canadian Journal of Mathematics 63(5):1161-1187 (2011)

Cited by in corpus (5)

• Harmonic analysis on quantum tori
• Schur and Fourier multipliers of an amenable group acting on non-commutative Lp-spaces
• Multilinear transference of Fourier and Schur multipliers acting on non-commutative $L_p$-spaces
• The local geometry of idempotent Schur multipliers
• A Marcinkiewicz Testing Criterion for Schur Multipliers