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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02725 |
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| _version_ | 1866913341486661632 |
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| author | Carro, María J. Naibo, Virginia Soria-Carro, María |
| author_facet | Carro, María J. Naibo, Virginia Soria-Carro, María |
| contents | We prove Hilbert transform identities involving conformal maps via the use of Rellich identity and the solution of the Neumann problem in a graph Lipschitz domain in the plane. We obtain as consequences new $L^2$-weighted estimates for the Hilbert transform, including a sharp bound for its norm as a bounded operator in weighted $L^2$ in terms of a weight constant associated to the Helson-Szegö theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rellich identities for the Hilbert transform Carro, María J. Naibo, Virginia Soria-Carro, María Functional Analysis Classical Analysis and ODEs 42B20 We prove Hilbert transform identities involving conformal maps via the use of Rellich identity and the solution of the Neumann problem in a graph Lipschitz domain in the plane. We obtain as consequences new $L^2$-weighted estimates for the Hilbert transform, including a sharp bound for its norm as a bounded operator in weighted $L^2$ in terms of a weight constant associated to the Helson-Szegö theorem. |
| title | Rellich identities for the Hilbert transform |
| topic | Functional Analysis Classical Analysis and ODEs 42B20 |
| url | https://arxiv.org/abs/2405.02725 |