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$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces (2312.00657v6)
Published 1 Dec 2023 in math.FA
Abstract: In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their $Lp -Lq$ 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 $Lp -Lq$ 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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