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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.04844 |
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| _version_ | 1866915774415765504 |
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| author | Curbera, Guillermo P. Okada, Susumu Ricker, Werner J. |
| author_facet | Curbera, Guillermo P. Okada, Susumu Ricker, Werner J. |
| contents | The action of the finite Hilbert transform defined on $L^\infty(-1,1)$ and taking its values in the Zygmund space $L_{\textnormal{exp}}(-1,1)$ is studied in detail. This is a reciprocal situation to the investigation recently undertaken in [11] of the finite Hilbert transform defined on the Zygumd space $L\textnormal{log} L(-1,1)$ and taking its values in $L^1(-1,1)$. The fact that both $L^\infty(-1,1)$ and $L_{\textnormal{exp}}(-1,1)$ fail to be separable generates new features not present in[11]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04844 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The finite Hilbert transform acting on $L^\infty$ Curbera, Guillermo P. Okada, Susumu Ricker, Werner J. Functional Analysis 44A15, 46E30, 47A53, 47B34 The action of the finite Hilbert transform defined on $L^\infty(-1,1)$ and taking its values in the Zygmund space $L_{\textnormal{exp}}(-1,1)$ is studied in detail. This is a reciprocal situation to the investigation recently undertaken in [11] of the finite Hilbert transform defined on the Zygumd space $L\textnormal{log} L(-1,1)$ and taking its values in $L^1(-1,1)$. The fact that both $L^\infty(-1,1)$ and $L_{\textnormal{exp}}(-1,1)$ fail to be separable generates new features not present in[11]. |
| title | The finite Hilbert transform acting on $L^\infty$ |
| topic | Functional Analysis 44A15, 46E30, 47A53, 47B34 |
| url | https://arxiv.org/abs/2602.04844 |