L_p-Multipliers on Quantum Tori

2015/12/02 by Éric Ricard, Ricard, Éric
Mathematics · #46L51 #47A30 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1512.01142

openalex publication_date 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_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.

Related

• A note on L^p-L^q boundedness of Fourier multipliers on noncommutative spaces
• L^p -L^q boundedness of Fourier multipliers on quantum Euclidean spaces
• Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
• Fourier multipliers and their applications to PDE on the quantum Euclidean space
• Noncommutative Coverings of Quantum Tori