ℓ2 Decoupling for Certain Surfaces of Finite Type in ℝ3.

In this article, we establish an ℓ2 decoupling inequality for the surface F 4 2 : = { (ξ 1 , ξ 2 , ξ 1 4 + ξ 2 4) : (ξ 1 , ξ 2) ∈ [ 0 , 1 ] 2 } associated with the decomposition adapted to finite type geometry from our previous work [Li, Z., Miao, C., Zheng, J.: A restriction estimate for a certain surface of finite type in ℝ3. J. Fourier Anal. Appl., 27(4), Paper No. 63, 24 pp. (2021)]. The key ingredients of the proof include the so-called generalized rescaling technique, an ℓ2 decoupling inequality for the surfaces { (ξ 1 , ξ 2 , ϕ 1 (ξ 1) + ξ 2 4) : (ξ 1 , ξ 2) ∈ [ 0 , 1 ] 2 } with ϕ1 being non-degenerate, reduction of dimension arguments and induction on scales. [ABSTRACT FROM AUTHOR]