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

Michael Ruzhansky (UGent) , Serikbol Shaimardan (UGent) and Kanat Tulenov (UGent)
(2024)
Author
Organization
Abstract
In this paper, we study H\"ormander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical inequalities such as Paley type, Hausdorff-Young-Paley, Hardy-Littlewood, and Logarithmic Sobolev inequalities on quantum tori. As applications we establish embedding theorems between Sobolev, Besov spaces as well as embeddings between Besov and Wiener and Beurling spaces on quantum tori. We also analyse $\beta$-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces on quantum tori. As an applications of the analysis, we also derive a version of the Nash inequality, and the time decay for solutions of a heat type equation.

Citation

Please use this url to cite or link to this publication:

MLA
Ruzhansky, Michael, et al. Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on  Quantum Tori, and Applications. 2024.
APA
Ruzhansky, M., Shaimardan, S., & Tulenov, K. (2024). Hörmander type Fourier multiplier theorem and Nikolskii inequality on  quantum tori, and applications.
Chicago author-date
Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2024. “Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on  Quantum Tori, and Applications.”
Chicago author-date (all authors)
Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2024. “Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on  Quantum Tori, and Applications.”
Vancouver
1.
Ruzhansky M, Shaimardan S, Tulenov K. Hörmander type Fourier multiplier theorem and Nikolskii inequality on  quantum tori, and applications. 2024;
IEEE
[1]
M. Ruzhansky, S. Shaimardan, and K. Tulenov, “Hörmander type Fourier multiplier theorem and Nikolskii inequality on  quantum tori, and applications,” 2024.
@article{01JHFCZVKGYYRFBJJPZYE53T5H,
  abstract     = {{  In this paper, we study H\"ormander type Fourier multiplier theorem and the
Nikolskii inequality on quantum tori. On the way to obtain these results, we
also prove some classical inequalities such as Paley type,
Hausdorff-Young-Paley, Hardy-Littlewood, and Logarithmic Sobolev inequalities
on quantum tori. As applications we establish embedding theorems between
Sobolev, Besov spaces as well as embeddings between Besov and Wiener and
Beurling spaces on quantum tori. We also analyse $\beta$-versions of Wiener and
Beurling spaces and their embeddings, and interpolation properties of all these
spaces on quantum tori. As an applications of the analysis, we also derive a
version of the Nash inequality, and the time decay for solutions of a heat type
equation.
}},
  author       = {{Ruzhansky, Michael and Shaimardan, Serikbol and Tulenov, Kanat}},
  language     = {{und}},
  title        = {{Hörmander type Fourier multiplier theorem and Nikolskii inequality on
  quantum tori, and applications}},
  year         = {{2024}},
}