$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909850939686912 |
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| author | Ruzhansky, M. Shaimardan, S. Tulenov, K. |
| author_facet | Ruzhansky, M. Shaimardan, S. Tulenov, K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00657 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces Ruzhansky, M. Shaimardan, S. Tulenov, K. Functional Analysis 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. |
| title | $L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.00657 |