The \(\overline\partial\)-Neumann operator on Lipschitz pseudoconvex domains with plurisubharmonic defining functions
If \(D\) is a bounded pseudoconvex Lipschitz domain in \(\mathbb{C}^n\) with a plurisubharmonic Lipschitz defining function, the authors prove that the \(\overline\partial\)-Neumann operator and the canonical Kohn solution operator of the \(\overline\partial\)-equation are bounded from the Sobolev space \(H^{1/2}(D)\) to itself. In a more general setting a slightly weaker result has been obtained by \textit{Bo Berndtsson} and \textit{Ph. Charpentier} [Math. Z. 235, 1-10 (2000; Zbl 0969.32015)] who proved that the Kohn operator and the Bergman projection are bounded on \(H^s\) for \(s< \eta/2\) provided that \(D\) has a defining function \(\rho\) such that \(-(-\rho)^\eta\) is plurisubharmonic.
bounded pseudoconvex Lipschitz domain in \(\mathbb{C}^n\)
plurisubharmonic Lipschitz defining function
scientific article; zbMATH DE number 1820826
scientific article