Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929546894245888 |
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| author | Harrington, Phillip S. |
| author_facet | Harrington, Phillip S. |
| contents | Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $L^2$ Sobolev regularity of the Bergman projection acting on $L^2$ sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds Harrington, Phillip S. Complex Variables 32U10, 32T35, 32Q28 Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $L^2$ Sobolev regularity of the Bergman projection acting on $L^2$ sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric. |
| title | Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds |
| topic | Complex Variables 32U10, 32T35, 32Q28 |
| url | https://arxiv.org/abs/2410.12715 |