Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains
Let $\Omega $ be a product domain in $\mathbb{C}^n, n\ge 2$, where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar{\partial }$ equation on $\Omega $ is bounded in $W^{k,p}(\Omega )$, $k\in \mathbb{Z}^+, 1
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Académie des sciences
2024-03-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.561/ |
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| author | Zhang, Yuan |
| author_facet | Zhang, Yuan |
| author_sort | Zhang, Yuan |
| collection | DOAJ |
| description | Let $\Omega $ be a product domain in $\mathbb{C}^n, n\ge 2$, where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar{\partial }$ equation on $\Omega $ is bounded in $W^{k,p}(\Omega )$, $k\in \mathbb{Z}^+, 1 |
| format | Article |
| id | doaj-art-667c769488b541429306a5a2958b894b |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-667c769488b541429306a5a2958b894b2025-02-07T11:16:25ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-03-01362G217117610.5802/crmath.56110.5802/crmath.561Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domainsZhang, Yuan0Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, USALet $\Omega $ be a product domain in $\mathbb{C}^n, n\ge 2$, where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar{\partial }$ equation on $\Omega $ is bounded in $W^{k,p}(\Omega )$, $k\in \mathbb{Z}^+, 1https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.561/canonical solution$\bar{\partial }$ equationBergman projectionproduct domainsSobolev regularity |
| spellingShingle | Zhang, Yuan Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains Comptes Rendus. Mathématique canonical solution $\bar{\partial }$ equation Bergman projection product domains Sobolev regularity |
| title | Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains |
| title_full | Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains |
| title_fullStr | Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains |
| title_full_unstemmed | Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains |
| title_short | Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains |
| title_sort | sobolev regularity of the canonical solutions to bar partial on product domains |
| topic | canonical solution $\bar{\partial }$ equation Bergman projection product domains Sobolev regularity |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.561/ |
| work_keys_str_mv | AT zhangyuan sobolevregularityofthecanonicalsolutionstobarpartialonproductdomains |