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arXiv · 0912.0841

On the weighted $\bar\partial$-Neumann problem on unbounded domains

Klaus Gansberger
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Abstract

Let $Ω$ be an unbounded, pseudoconvex domain in $\Bbb C^n$ and let $φ$ be a $\mathcal C^2$-weight function plurisubharmonic on $Ω$. We show both necessary and sufficient conditions for existence and compactness of a weighted $\bar\partial$-Neumann operator $N_φ$ on the space $L^2_{(0,1)}(Ω,e^{-φ})$ in terms of the eigenvalues of the complex Hessian $(\partial ^2φ/\partial z_j\partial\bar z_k)_{j,k}$ of the weight. We also give some applications to the unweighted $\bar\partial$-Neumann problem on unbounded domains.

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Klaus Gansberger. 2009-12-04. On the weighted $\bar\partial$-Neumann problem on unbounded domains. https://arxiv.org/abs/0912.0841

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