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arXiv · 1905.04238

The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders

Phillip Harrington·Bingyuan Liu
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Abstract

Let $\Omega\subset\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\in\mathbb{N}$, we give a sufficient condition to estimate the $\bar\partial$-Neumann operator in the Sobolev space $W^k(\Omega)$. The key feature of our results is a precise formula for $k$ in terms of the geometry of the boundary of $\Omega$.

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Phillip Harrington, Bingyuan Liu. 2019-05-10. The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders. https://arxiv.org/abs/1905.04238

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