Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains

Yuan Zhang

doi:10.5802/crmath.561

Article de recherche - Analyse et géométrie complexes

Sobolev regularity of the canonical solutions to

\bar{\partial}

on product domains

Yuan Zhang ¹

¹ Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, USA

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 171-176.

Résumé

Let $Ω$ be a product domain in $ℂ^{n}, n \geq 2$ , where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar{\partial}$ equation on $Ω$ is bounded in $W^{k, p} (Ω)$ , $k \in ℤ^{+}, 1 < p < \infty$ . This Sobolev regularity is sharp in view of Kerzman-type examples.

Reçu le : 2022-11-21
Révisé le : 2023-06-23
Accepté le : 2023-09-01
Publié le : 2024-03-07

DOI : 10.5802/crmath.561

Classification : 32W05, 32A25, 32A36
Mots clés : canonical solution, $\bar{\partial }$ equation, Bergman projection, product domains, Sobolev regularity

Affiliations des auteurs :

Yuan Zhang ¹

¹ Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Yuan Zhang},
     title = {Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {171--176},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.561},
     language = {en},
}

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Yuan Zhang. Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 171-176. doi : 10.5802/crmath.561. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.561/

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