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

In this paper, we study the restriction estimate for a certain surface of finite type in $\mathbb{R}^3$, and partially improves results Buschenhenke-M\"{u}ller-Vargas. The key ingredients proof include so called generalized rescaling technique based on decomposition adapted to geometry, decoupling inequality reduction dimension arguments.