A Restriction Estimate for a Certain Surface of Finite Type in $${\mathbb {R}}^3$$

Abstract

In this paper, we study the restriction estimate for a certain surface of finite type in $\mathbb{R}^3$, and partially improves the results of Buschenhenke-M\"{u}ller-Vargas. 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.