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

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 $\Omega$.

Cited by in corpus (1)

• The Diederich--Fornæss index and the regularities on the $\bar{\partial }$-Neumann problem