Projections onto $L^p$-Bergman spaces of Reinhardt Domains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908380734423040 |
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| author | Chakrabarti, Debraj Edholm, Luke D. |
| author_facet | Chakrabarti, Debraj Edholm, Luke D. |
| contents | For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the kernel is shown to be absolutely bounded projection on the $L^p$-Bergman space on a class of domains where the $L^p$-boundedness of the Bergman projection fails for certain $p \neq 2$. As an application, we identify the duals of these $L^p$-Bergman spaces with weighted Bergman spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10005 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Projections onto $L^p$-Bergman spaces of Reinhardt Domains Chakrabarti, Debraj Edholm, Luke D. Complex Variables Functional Analysis 32A36, 46B15, 32A70, 32A25 For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the kernel is shown to be absolutely bounded projection on the $L^p$-Bergman space on a class of domains where the $L^p$-boundedness of the Bergman projection fails for certain $p \neq 2$. As an application, we identify the duals of these $L^p$-Bergman spaces with weighted Bergman spaces. |
| title | Projections onto $L^p$-Bergman spaces of Reinhardt Domains |
| topic | Complex Variables Functional Analysis 32A36, 46B15, 32A70, 32A25 |
| url | https://arxiv.org/abs/2303.10005 |