On Fourier restriction and the Newton polygon
On Fourier restriction and the Newton polygon
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论傅里叶限制和牛顿多边形
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Á. Magyar
中科院分区：
文献类型：
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作者：
Á. Magyar
本文证明了Fourier变换对R3中解析曲面S =（x，f（x））的限制的局部Lp → L2界.它被发现，指数的范围是由所谓的牛顿多边形的距离，与f，除了当主准齐次部分f（x）包含一个高的多重性的因素。证明是基于Phong-Stein和Rychkov的方法，适用于标量振荡积分。
Local L P → L 2 bounds are proved for the restriction of the Fourier transform to analytic surfaces of the form S = (x, f(x)) in R 3 . It is found that the range of exponents is determined by the so-called distance of the Newton polygon, associated to f, except when the principal quasi-homogeneous part of f(x) contains a factor of high multiplicity. The proofs are based on the method of Phong-Stein and Rychkov, adapted to scalar oscillatory integrals.