In this paper, we study the restriction estimate for a certain surface of finite type in \({\mathbb {R}}^3\), and partially improve the results of Buschenhenke–Müller–Vargas (Anal PDE 10:817–891, 2017). The key ingredients of the proof include the so-called generalized rescaling technique based on a decomposition adapted to finite type geometry, a decoupling inequality and reduction of dimension arguments.

中文翻译：

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$${\mathbb {R}}^3$$ R 3 中某个有限类型表面的限制估计

在本文中，我们研究了\({\mathbb {R}}^3\) 中某个有限类型曲面的约束估计，并部分改进了 Buschenhenke–Müller–Vargas (Anal PDE 10:817–891 , 2017)。证明的关键要素包括基于适用于有限类型几何的分解的所谓广义重新缩放技术、解耦不等式和维度参数的减少。