The $\bar {\partial }$-Neumann operator on Lipschitz $q$-pseudoconvex domains

Saber, Sayed

Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 721-731

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-011-0021-2

Classification : 32F10, 32W05
Keywords: Sobolev estimate; $\bar \partial $ and $\bar \partial $-Neumann operator; $q$-pseudoconvex domains; Lipschitz domains

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