l^(2) Decoupling for Certain Surfaces of Finite Type in R^(3)

作     者：Zhuo Ran LI Ji Qiang ZHENG Zhuo Ran LI;Ji Qiang ZHENG

作者机构：School of Mathematics and StatisticsYancheng Teachers UniversityYancheng 224002P.R.China Institute of Applied Physics and Computational MathematicsP.O.Box 8009Beijing 100088P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第8期

页      面：1442-1458页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by National key R&D program of China(Grant No.2021YFA1002500) NSFC(Grant No.12271051) PFCAEP project(Grant No.YZJJLX201901) 

主　　题：Decoupling inequality finite type reduction of dimension arguments induction on scales 

摘      要：In this article,we establish an 2 decoupling inequality for the surface F_(4)^(2):={(ξ1,ξ2,ξ_(1)^(4)+ξ_(2)^(4)):(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 R^(3).*** ***.,27(4),Paper No.63,24 pp.(2021)].The key ingredients of the proof include the so-called generalized rescaling technique,an l^(2) decoupling inequality for the surfaces{(ξ1,ξ2,φ1(ξ1)+ξ42):(ξ1,ξ2)∈[0,1]^(2)}with φ1 being non-degenerate,reduction of dimension arguments and induction on scales.