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Keywords:
Sobolev estimate; $\bar \partial $ and $\bar \partial $-Neumann operator; $q$-pseudoconvex domains; Lipschitz domains
Sobolev estimate; $\bar \partial $ and $\bar \partial $-Neumann operator; $q$-pseudoconvex domains; Lipschitz domains
Summary:
On a bounded $q$-pseudoconvex domain $\Omega $ in $\mathbb {C}^{n}$ with a Lipschitz boundary, we prove that the $\bar {\partial }$-Neumann operator $N$ satisfies a subelliptic $(1/2)$-estimate on $\Omega $ and $N$ can be extended as a bounded operator from Sobolev $(-1/2)$-spaces to Sobolev $(1/2)$-spaces.
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