Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| _version_ | 1866913700867211264 |
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| author | Khanh, Tran Vu Raich, Andrew |
| author_facet | Khanh, Tran Vu Raich, Andrew |
| contents | The purpose of this paper is to prove that if a pseudoconvex domains $Ω\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman projection has local $L^p$-Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform $L^2$ pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that $h$-extendible domains satisfy our hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1406_6532 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type Khanh, Tran Vu Raich, Andrew Complex Variables 32A25, 32T25, 32W05, 32A50 The purpose of this paper is to prove that if a pseudoconvex domains $Ω\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman projection has local $L^p$-Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform $L^2$ pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that $h$-extendible domains satisfy our hypotheses. |
| title | Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type |
| topic | Complex Variables 32A25, 32T25, 32W05, 32A50 |
| url | https://arxiv.org/abs/1406.6532 |