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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11600 |
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| _version_ | 1866917898395582464 |
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| author | Ghorbanalizadeh, Arash Seraji, Reza Roohi |
| author_facet | Ghorbanalizadeh, Arash Seraji, Reza Roohi |
| contents | In this paper, by using continuous Hilbert transform and maximal operator boundedness property in the variable Lebesgue space $ L^{p(\cdot)}(\mathbb{R}) $ we show that the discrete Hilbert transform is bounded in the variable discrete Lebesgue space $ \ell^{p_n}(\mathbb{Z}) $. We show that the discrete Mikhlin multiplier $ \mathcal{T}_m $ is a bounded operator on $ \ell^{p_n}(\mathbb{Z}) $ when $ 1<\underline{p}_n<\bar{p}_n<\infty $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete Hilbert Transform And Discrete Mikhlin Multiplier On Discrete Variable Lebesgue Space Ghorbanalizadeh, Arash Seraji, Reza Roohi Functional Analysis In this paper, by using continuous Hilbert transform and maximal operator boundedness property in the variable Lebesgue space $ L^{p(\cdot)}(\mathbb{R}) $ we show that the discrete Hilbert transform is bounded in the variable discrete Lebesgue space $ \ell^{p_n}(\mathbb{Z}) $. We show that the discrete Mikhlin multiplier $ \mathcal{T}_m $ is a bounded operator on $ \ell^{p_n}(\mathbb{Z}) $ when $ 1<\underline{p}_n<\bar{p}_n<\infty $. |
| title | Discrete Hilbert Transform And Discrete Mikhlin Multiplier On Discrete Variable Lebesgue Space |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2501.11600 |