Abstract Let be a bounded pseudoconvex domain with smooth boundary. For each we give a sufficient condition to estimate the -Neumann operator in the Sobolev space The key feature of our results is a precise formula for k in terms of the geometry of the boundary of Ω. It also shows the bound in the precise formula for Sobolev estimates of order k is comparably reciprocal of the Sobolev order k.

中文翻译：

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带有 Sobolev 估计的 ∂¯-Neumann 算子直到有限阶

Abstract 让 是一个边界平滑的有界伪凸域。对于每一个，我们都给出了一个充分条件来估计 Sobolev 空间中的 -Neumann 算子。我们结果的关键特征是根据 Ω 边界的几何形状计算 k 的精确公式。它还显示了 Sobolev 阶 k 估计的精确公式中的界限是 Sobolev 阶 k 的倒数。