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

Michael Ruzhansky (UGent) , Serikbol Shaimardan (UGent) and Kanat Tulenov (UGent)
(2023)
Author
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.

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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}},
}