$l^2$ Decoupling for certain degenerate surfaces in ${\mathbb{R}}^4$

In this article, we aim to study decoupling inequality for a specific degenerate hypersurface in ${\mathbb{R}}^4$. Inspired by the work of Bourgain–Demeter and Li–Zheng, we consider the hypersurface ${\mathcal{S}}_4^3:=\{({\xi }_1,{\xi }_2,{\xi }_3,{\xi }_1^4+{\xi }_2^4+{\xi }_3^4):0\le {\xi }_j\le 1,\text{for }j=1,2,3\}$ in ${\mathbb{R}}^4$ and study decoupling estimates.