Cauchy transforms and Szegő projections in dual Hardy spaces: inequalities and Möbius invariance
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908380864446464 |
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| author | Barrett, David E. Edholm, Luke D. |
| author_facet | Barrett, David E. Edholm, Luke D. |
| contents | Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform $\bf{C}$ from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of $\bf{C}$ is produced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cauchy transforms and Szegő projections in dual Hardy spaces: inequalities and Möbius invariance Barrett, David E. Edholm, Luke D. Complex Variables 30C40 (Primary), 30H10, 30E20, 32A25, 46E22 (Secondary) Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform $\bf{C}$ from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of $\bf{C}$ is produced. |
| title | Cauchy transforms and Szegő projections in dual Hardy spaces: inequalities and Möbius invariance |
| topic | Complex Variables 30C40 (Primary), 30H10, 30E20, 32A25, 46E22 (Secondary) |
| url | https://arxiv.org/abs/2407.13033 |