Hardy Spaces for a Class of Singular Domains
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866911863586947072 |
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| author | Gallagher, Anne-Katrin Gupta, Purvi Lanzani, Loredana Vivas, Liz |
| author_facet | Gallagher, Anne-Katrin Gupta, Purvi Lanzani, Loredana Vivas, Liz |
| contents | We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filtration, various aspects of which are studied in specific settings. For punctured planar domains, we prove a generalization of a famous rigidity lemma of Kerzman and Stein. A stabilization phenomenon is observed for egg domains. Finally, using proper holomorphic maps, we derive a filtration of Hardy spaces for certain power-generalized Hartogs triangles, although these domains fall outside the scope of the original framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_02466 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hardy Spaces for a Class of Singular Domains Gallagher, Anne-Katrin Gupta, Purvi Lanzani, Loredana Vivas, Liz Complex Variables Functional Analysis 30H10, 42B30, 46E22, 32A25, 32Q02 We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filtration, various aspects of which are studied in specific settings. For punctured planar domains, we prove a generalization of a famous rigidity lemma of Kerzman and Stein. A stabilization phenomenon is observed for egg domains. Finally, using proper holomorphic maps, we derive a filtration of Hardy spaces for certain power-generalized Hartogs triangles, although these domains fall outside the scope of the original framework. |
| title | Hardy Spaces for a Class of Singular Domains |
| topic | Complex Variables Functional Analysis 30H10, 42B30, 46E22, 32A25, 32Q02 |
| url | https://arxiv.org/abs/2009.02466 |