Characterization of the weak-type boundedness of the Hilbert transform on weighted Lorentz spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916117677604864 |
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| author | Agora, Elona Carro, María J. Soria, Javier |
| author_facet | Agora, Elona Carro, María J. Soria, Javier |
| contents | We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $Λ^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of $H$ on weighted Lebesgue spaces $L^p(u)$ and Muckenhoupt weights $A_p$, and the theory on classical Lorentz spaces $Λ^p(w)$ and Ariño Muckenhoupt weights $B_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of the weak-type boundedness of the Hilbert transform on weighted Lorentz spaces Agora, Elona Carro, María J. Soria, Javier Classical Analysis and ODEs 26D10, 42A50 We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $Λ^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of $H$ on weighted Lebesgue spaces $L^p(u)$ and Muckenhoupt weights $A_p$, and the theory on classical Lorentz spaces $Λ^p(w)$ and Ariño Muckenhoupt weights $B_p$. |
| title | Characterization of the weak-type boundedness of the Hilbert transform on weighted Lorentz spaces |
| topic | Classical Analysis and ODEs 26D10, 42A50 |
| url | https://arxiv.org/abs/2402.04877 |