- Author
- Michael Ruzhansky (UGent) , Serikbol Shaimardan (UGent) and Kanat Tulenov (UGent)
- Organization
- 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.
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JHFCQ371JYJTYY78G2712GDJ
- MLA
- Ruzhansky, Michael, et al. $L^p -L^q$ Boundedness of Fourier Multipliers on Quantum Euclidean Spaces. 2023.
- APA
- Ruzhansky, M., Shaimardan, S., & Tulenov, K. (2023). $L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces.
- Chicago author-date
- Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2023. “$L^p -L^q$ Boundedness of Fourier Multipliers on Quantum Euclidean Spaces.”
- Chicago author-date (all authors)
- Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2023. “$L^p -L^q$ Boundedness of Fourier Multipliers on Quantum Euclidean Spaces.”
- Vancouver
- 1.Ruzhansky M, Shaimardan S, Tulenov K. $L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces. 2023;
- IEEE
- [1]M. Ruzhansky, S. Shaimardan, and K. Tulenov, “$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces,” 2023.
@article{01JHFCQ371JYJTYY78G2712GDJ, 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. }}, author = {{Ruzhansky, Michael and Shaimardan, Serikbol and Tulenov, Kanat}}, language = {{und}}, title = {{$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces}}, year = {{2023}}, }