$L_p$-Multipliers on Quantum Tori

Abstract

It was shown by Chen, Xu and Yin that completely bounded Fourier multipliers on noncommutative $L_p$-spaces of quantum tori $\mathbb T^d_\theta$ do not depend on the parameter $\theta$. We establish that the situation is somehow different for bounded multipliers. The arguments are based on transference from the commutative torus.