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 previ...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).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 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.展开更多
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...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.展开更多
基金Supported by National key R&D program of China(Grant No.2021YFA1002500),NSFC(Grant No.12271051),PFCAEP project(Grant No.YZJJLX201901)。
文摘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).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 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.
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)。
文摘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.
