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

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.

arXiv comment27 (Some revision is done) Accepted to Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat

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Cited by in corpus (1)

• Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications