Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913637175656448 |
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| author | Lai, Xudong Xiong, Xiao Zhang, Yue |
| author_facet | Lai, Xudong Xiong, Xiao Zhang, Yue |
| contents | For $1<p<\infty$, we establish the $L_{p}$ boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori $L_{p}(\mathbb{T}^{d}_θ)$, and quantum Euclidean space $L_{p}(\mathbb{R}^{d}_θ)$. In particular, the norm constants in both cases are independent of the dimension $d$ when $2\leq p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space Lai, Xudong Xiong, Xiao Zhang, Yue Operator Algebras Classical Analysis and ODEs 42B20, 42B25, 46L52, 46E40 For $1<p<\infty$, we establish the $L_{p}$ boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori $L_{p}(\mathbb{T}^{d}_θ)$, and quantum Euclidean space $L_{p}(\mathbb{R}^{d}_θ)$. In particular, the norm constants in both cases are independent of the dimension $d$ when $2\leq p<\infty$. |
| title | Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space |
| topic | Operator Algebras Classical Analysis and ODEs 42B20, 42B25, 46L52, 46E40 |
| url | https://arxiv.org/abs/2501.03107 |