Carleson Measures, Vanishing Mean Oscillation and Critical Points
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911185911152640 |
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| author | Bellavita, Carlo Nicolau, Artur Stylogiannis, Georgios |
| author_facet | Bellavita, Carlo Nicolau, Artur Stylogiannis, Georgios |
| contents | Given a finite positive Borel measure $μ$ in the open unit disc of the complex plane, we construct a bounded outer function $E$ whose boundary values have vanishing mean oscillation such that $|E| μ$ is a vanishing Carleson measure. As an application it is shown that given any function in a Hardy space, there exists a bounded analytic function in the unit disc whose boundary values have vanishing mean oscillation, with the same critical points and multiplicities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_26338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleson Measures, Vanishing Mean Oscillation and Critical Points Bellavita, Carlo Nicolau, Artur Stylogiannis, Georgios Complex Variables Classical Analysis and ODEs Primary: 30H35, Secondary: 30H10, 30H20, 30H50, 47G10 Given a finite positive Borel measure $μ$ in the open unit disc of the complex plane, we construct a bounded outer function $E$ whose boundary values have vanishing mean oscillation such that $|E| μ$ is a vanishing Carleson measure. As an application it is shown that given any function in a Hardy space, there exists a bounded analytic function in the unit disc whose boundary values have vanishing mean oscillation, with the same critical points and multiplicities. |
| title | Carleson Measures, Vanishing Mean Oscillation and Critical Points |
| topic | Complex Variables Classical Analysis and ODEs Primary: 30H35, Secondary: 30H10, 30H20, 30H50, 47G10 |
| url | https://arxiv.org/abs/2509.26338 |