Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on Quantum Tori, and Applications


Ruzhansky M. Shaimardan S. Tulenov K.
February 2026Birkhauser

Journal of Fourier Analysis and Applications
2026#32Issue 1

In this paper, we study Hörmander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical inequalities such as the Paley, Hausdorff-Young-Paley, Hardy-Littlewood, and Logarithmic Sobolev inequalities on quantum tori. As applications we establish embedding theorems between Sobolev, Besov spaces as well as embeddings between Besov and Wiener and Beurling spaces on quantum tori. We also analyse β-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces on quantum tori. As an application of the study, we also derive a version of the Nash inequality, and the time decay for solutions of a heat type equation.

Besov space , Hausdorff-Young inequality , Hörmander Fourier multiplier , Logarithmic Sobolev inequality , Nikolskii inequality , Quantum tori , Wiener and Beurling spaces

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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling

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