$L_p$-Multipliers on Quantum Tori

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

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