?2 Decoupling for Certain Surfaces of Finite Type in R3

In this article,we establish an l2decoupling inequality for the surface F42:={(ξ1,ξ2,ξ14+ξ24):(ξ1,ξ2)∈[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 l2decoupling inequality for the surfaces{(ξ1,ξ2,φ1(ξl)+ξ24):(ξ1,ξ2)∈[0,1]2}with φ1being non-degenerate,reduction of dimension arguments and induction on scales.