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arXiv · 2312.00657

$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces

M. Ruzhansky·S. Shaimardan·K. Tulenov
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Abstract

In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their $L^p -L^q$ boundedness. On the way to get these results, we prove Paley, Hausdorff-Young-Paley, and Hardy-Littlewood inequalities on the quantum Euclidean space. As applications, we establish the $L^p -L^q$ estimate for the heat semigroup and Sobolev embedding theorem on quantum Euclidean spaces. We also obtain quantum analogues of the logarithmic Sobolev and Nash type inequalities.

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M. Ruzhansky, S. Shaimardan, K. Tulenov. 2023-12-01. $L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces. https://doi.org/10.1007/s13398-025-01798-x

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