Boundedness of the Hilbert transform on weighted Lorentz spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909098835968000 |
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| author | Agora, Elona Carro, María J. Soria, Javier |
| author_facet | Agora, Elona Carro, María J. Soria, Javier |
| contents | We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $Λ^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete characterization of the weak-type boundedness of both $H$ and $H^*$, whenever $u\in A_1$. For the strong-type case, we also get the characterization of both operators when $p>1$. Applications to the case of Lorentz spaces $L^{p,q}(u)$ are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness of the Hilbert transform on weighted Lorentz spaces Agora, Elona Carro, María J. Soria, Javier Classical Analysis and ODEs 26D10, 42EB10 We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $Λ^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete characterization of the weak-type boundedness of both $H$ and $H^*$, whenever $u\in A_1$. For the strong-type case, we also get the characterization of both operators when $p>1$. Applications to the case of Lorentz spaces $L^{p,q}(u)$ are presented. |
| title | Boundedness of the Hilbert transform on weighted Lorentz spaces |
| topic | Classical Analysis and ODEs 26D10, 42EB10 |
| url | https://arxiv.org/abs/2402.05299 |