检索结果-南通市图书馆

L^(2)Schrödinger Maximal Estimates Associated with finite type Phases in R^(2)

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第11期40卷 2809-2839页

作者： Zhuo Ran LI Jun Yan ZHAO Teng Fei ZHAO Department of Mathematics Taizhou UniversityTaizhou225300P.R.China School of Mathematical Sciences Zhejiang Normal UniversityJinhua321004P.R.China School of Mathematics and Physics University of Science and Technology BeijingBeijing100083P.R.China

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 ***[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 *** 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 *** notice that our Theorem 1.1 has some similarities with the results in[8].However,their results do not cover *** 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

l^(2) Decoupling for Certain Surfaces of finite type in R^(3)

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2023年第8期39卷 1442-1458页

作者： Zhuo Ran LI Ji Qiang ZHENG School of Mathematics and Statistics Yancheng Teachers UniversityYancheng 224002P.R.China Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088P.R.China

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.

关键词： Decoupling inequality finite type reduction of dimension arguments induction on scales

Cotilting modules with finite left perpendicular categories Dedicated to Professor Feng Keqin on the Occasion of his 70th Birthday

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2012年第1期55卷 93-98页

作者： LI ZhiWei ZHANG Pu Department of Mathematics Shanghai Jiao Tong UniversityShanghai 200240China

We characterize a cotilting module T such that the left perpendicular category ⊥ T is of finite type.

关键词： cotilting module resolving module finite type

L^p Boundedness of Marcinkiewicz Integrals with H^1 Kernels

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2008年第6期24卷 1031-1038页

作者： Leslie C.CHENG Department of Mathematics Bryn Mawr CollegeBryn MawrPA 19010USA

We establish the L^p boundedness of Marcinkiewicz integral operators with kernels in theHardy space on a compact submanifold of finite type. Previously such boundedness properties were obtained when the submanifold is a sphere. Our result shows that what matters is not the symmetry, but a certain type of curvature property of the submanifold.

关键词： Marcinkiewicz integrals Hardy space finite type

Oscillatory integrals for phase functions having certain degenerate critical points

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2008年第3期51卷 474-480页

作者： Jinmyong KIM Department of Mathematics.Huazhong University of Science and Technology

The paper is concerned with oscillatory integrals for phase functions having certain de- generate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol.

关键词： oscillatory integral phase function finite type 42B10