$L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains
On a bounded $q$-pseudoconvex domain $\Omega $ in $\mathbb{C}^{n}$ with Lipschitz boundary $b\Omega $, we prove the $L^2$ existence theorems of the $\overline{\partial }_b$-operator on $b\Omega $. This yields the closed range property of $\overline{\partial }_b$ and its adjoint $\overline{\partial }...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.43/ |
| _version_ | 1797651542292037632 |
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| author | Saber, Sayed |
| author_facet | Saber, Sayed |
| author_sort | Saber, Sayed |
| collection | DOAJ |
| description | On a bounded $q$-pseudoconvex domain $\Omega $ in $\mathbb{C}^{n}$ with Lipschitz boundary $b\Omega $, we prove the $L^2$ existence theorems of the $\overline{\partial }_b$-operator on $b\Omega $. This yields the closed range property of $\overline{\partial }_b$ and its adjoint $\overline{\partial }_b^*$. As an application, we establish the $L^2$-existence theorems and regularity theorems for the $\overline{\partial }_b$-Neumann operator. |
| first_indexed | 2024-03-11T16:17:18Z |
| format | Article |
| id | doaj.art-703cb9ace8944e0f93f07cf87334c804 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:18Z |
| publishDate | 2020-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-703cb9ace8944e0f93f07cf87334c8042023-10-24T14:19:02ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-07-01358443545810.5802/crmath.4310.5802/crmath.43$L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domainsSaber, Sayed0Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, EgyptOn a bounded $q$-pseudoconvex domain $\Omega $ in $\mathbb{C}^{n}$ with Lipschitz boundary $b\Omega $, we prove the $L^2$ existence theorems of the $\overline{\partial }_b$-operator on $b\Omega $. This yields the closed range property of $\overline{\partial }_b$ and its adjoint $\overline{\partial }_b^*$. As an application, we establish the $L^2$-existence theorems and regularity theorems for the $\overline{\partial }_b$-Neumann operator.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.43/ |
| spellingShingle | Saber, Sayed $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains Comptes Rendus. Mathématique |
| title | $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains |
| title_full | $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains |
| title_fullStr | $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains |
| title_full_unstemmed | $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains |
| title_short | $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains |
| title_sort | l 2 estimates and existence theorems for protect overline partial b on lipschitz boundaries of q pseudoconvex domains |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.43/ |
| work_keys_str_mv | AT sabersayed l2estimatesandexistencetheoremsforprotectoverlinepartialbonlipschitzboundariesofqpseudoconvexdomains |