$L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains

Saber, Sayed

doi:10.5802/crmath.43

Analyse complexe

L^{2}

estimates and existence theorems for

{\bar{\partial}}_{b}

on Lipschitz boundaries of

Q

-pseudoconvex domains

Saber, Sayed ¹

¹ Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt

Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 435-458.

Résumé

On a bounded $q$ -pseudoconvex domain $Ω$ in $ℂ^{n}$ with Lipschitz boundary $b Ω$ , we prove the $L^{2}$ existence theorems of the ${\bar{\partial}}_{b}$ -operator on $b Ω$ . This yields the closed range property of ${\bar{\partial}}_{b}$ and its adjoint ${\bar{\partial}}_{b}^{*}$ . As an application, we establish the $L^{2}$ -existence theorems and regularity theorems for the ${\bar{\partial}}_{b}$ -Neumann operator.

Reçu le : 2019-05-01
Accepté le : 2020-03-24
Publié le : 2020-07-28

DOI : 10.5802/crmath.43

Classification : 35J20, 35J25, 35J60

Affiliations des auteurs :

Saber, Sayed ¹

¹ Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt

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     author = {Saber, Sayed},
     title = {$L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on {Lipschitz} boundaries of $Q$-pseudoconvex domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {435--458},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     year = {2020},
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     url = {http://www.numdam.org/articles/10.5802/crmath.43/}
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Saber, Sayed. $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 435-458. doi : 10.5802/crmath.43. http://www.numdam.org/articles/10.5802/crmath.43/

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