Comptes Rendus
Article de recherche - Analyse et géométrie complexes
Sobolev regularity of the canonical solutions to ¯ on product domains
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 171-176.

Let Ω be a product domain in n ,n2, where each slice has smooth boundary. We observe that the canonical solution operator for the ¯ equation on Ω is bounded in W k,p (Ω), k + ,1<p<. This Sobolev regularity is sharp in view of Kerzman-type examples.

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DOI : 10.5802/crmath.561
Classification : 32W05, 32A25, 32A36
Mots clés : canonical solution, $\bar{\partial }$ equation, Bergman projection, product domains, Sobolev regularity

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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     title = {Sobolev regularity of the canonical solutions to $\bar{\partial }$ on product domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {171--176},
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     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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