Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
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| Format: | Preprint |
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2024
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| _version_ | 1866918240136986624 |
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| author | Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat |
| author_facet | Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat Functional Analysis 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. |
| title | Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.17353 |