A maximal restriction theorem and Lebesgue points of functions in $mathcal F(L^p)$
A maximal restriction theorem and Lebesgue points of functions in $mathcal F(L^p)$
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$mathcal F(L^p)$ 中函数的最大限制定理和勒贝格点
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发表时间：
2016
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通讯作者：
James Wright
中科院分区：
文献类型：
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作者：
D. Muller;F. Ricci;James Wright
傅立叶限制定理的研究是由E.M. Stein，通常描述Lp（Rn）中函数f的傅里叶变换到给定子簇S的限制的Lq-范数的一族先验估计，赋予适当的测度。这样的估计允许定义限制Rf的傅立叶变换的Lp函数S在算子理论意义上。在这篇文章中，我们开始研究的问题是什么是"内在的”点态关系之间的Rf和傅里叶变换的f，通过看曲线在平面上，例如与非零曲率。为此，我们绑定合适的极大算子，包括Hardy-Littlewood极大函数的傅里叶变换f限制到S。
Fourier restriction theorems, whose study had been initiated by E.M. Stein, usually describe a family of a priori estimates of the Lq-norm of the restriction of the Fourier transform of a function f in Lp(Rn) to a given subvariety S, endowed with a suitable measure. Such estimates allow to define the restriction Rf of the Fourier transform of an Lp-function to S in an operator theoretic sense. In this article, we begin to investigate the question what is the „intrinsic" pointwise relation between Rf and the Fourier transform of f, by looking at curves in the plane, for instance with non-vanishing curvature. To this end, we bound suitable maximal operators, including the Hardy–Littlewood maximal function of the Fourier transform of f restricted to S.