L^(2)Schrödinger Maximal Estimates Associated with Finite Type Phases in R^(2)  

作　　者：Zhuo Ran LI Jun Yan ZHAO Teng Fei ZHAO 

机构地区：[1]Department of Mathematics,Taizhou University,Taizhou,225300,P.R.China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,321004,P.R.China [3]School of Mathematics and Physics,University of Science and Technology Beijing,Beijing,100083,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第11期2809-2839,共31页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.12101562,12101040,12271051 and 12371239);by a grant from the China Scholarship Council(CSC)。

摘　　要：In this paper,we establish Schrödinger maximal estimates associated with the finite type phaseФ(ξ_(1),ξ_(2)):=ξ_(1)^(m)+ξ_(2)^(m),where m≥4 is an even number.Following[12],we prove an L2 fractal restriction estimate associated with the surface{(ξ_(1),ξ_(2),Ф(ξ_(1),ξ_(2))):(ξ_(1),ξ_(2)∈[0,]^(2)}as the main result,which also gives results on the average Fourier decay of fractal measures associated with these surfaces.The key ingredients of the proof include the rescaling technique from[16],Bourgain-Demeter’sℓ^(2)decoupling inequality,the reduction of dimension arguments from[17]and induction on scales.We notice that our Theorem 1.1 has some similarities with the results in[8].However,their results do not cover ours.Their arguments depend on the positive definiteness of the Hessian matrix of the phase function,while our phase functions are degenerate.

关 键 词：Pointwise convergence finite type DECOUPLING reduction of dimension arguments 

分 类 号：O175.2[理学—数学]