On a bounded -pseudoconvex domain in with Lipschitz boundary , we prove the existence theorems of the -operator on . This yields the closed range property of and its adjoint . As an application, we establish the -existence theorems and regularity theorems for the -Neumann operator.
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@article{CRMATH_2020__358_4_435_0, 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}, number = {4}, year = {2020}, doi = {10.5802/crmath.43}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/crmath.43/} }
TY - JOUR AU - Saber, Sayed TI - $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains JO - Comptes Rendus. Mathématique PY - 2020 SP - 435 EP - 458 VL - 358 IS - 4 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.43/ DO - 10.5802/crmath.43 LA - en ID - CRMATH_2020__358_4_435_0 ER -
%0 Journal Article %A Saber, Sayed %T $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains %J Comptes Rendus. Mathématique %D 2020 %P 435-458 %V 358 %N 4 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.43/ %R 10.5802/crmath.43 %G en %F CRMATH_2020__358_4_435_0
Saber, Sayed. $L^2$ estimates and existence theorems for $\protect \overline{\partial }_b$ on Lipschitz boundaries of $Q$-pseudoconvex domains. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 435-458. doi : 10.5802/crmath.43. http://archive.numdam.org/articles/10.5802/crmath.43/
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