Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
- Author
- Michael Ruzhansky (UGent) , Serikbol Shaimardan (UGent) and Kanat Tulenov (UGent)
- Organization
- Project
- Abstract
- In this paper, we study Hörmander 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 β-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.
- Keywords
- Quantum tori, Hörmander Fourier multiplier, Nikolskii inequality, Hausdorff-Young inequality, Logarithmic Sobolevin equality, Besov space, Wiener and Beurling spaces
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JHFCZVKGYYRFBJJPZYE53T5H
- MLA
- Ruzhansky, Michael, et al. “Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on Quantum Tori, and Applications.” ArXiv, 2024, doi:10.48550/arXiv.2402.17353.
- APA
- Ruzhansky, M., Shaimardan, S., & Tulenov, K. (2024). Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications. https://doi.org/10.48550/arXiv.2402.17353
- Chicago author-date
- Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2024. “Hörmander Type Fourier Multiplier Theorem and Nikolskii Inequality on Quantum Tori, and Applications.” ArXiv. https://doi.org/10.48550/arXiv.2402.17353.
- 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.” ArXiv. doi:10.48550/arXiv.2402.17353.
- Vancouver
- 1.Ruzhansky M, Shaimardan S, Tulenov K. Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications. arXiv. 2024.
- IEEE
- [1]M. Ruzhansky, S. Shaimardan, and K. Tulenov, “Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications,” arXiv. 2024.
@misc{01JHFCZVKGYYRFBJJPZYE53T5H,
abstract = {{In this paper, we study Hörmander 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 β-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}},
keywords = {{Quantum tori,Hörmander Fourier multiplier,Nikolskii inequality,Hausdorff-Young inequality,Logarithmic Sobolevin equality,Besov space,Wiener and Beurling spaces}},
language = {{eng}},
pages = {{42}},
series = {{arXiv}},
title = {{Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications}},
url = {{http://doi.org/10.48550/arXiv.2402.17353}},
year = {{2024}},
}
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