Sharp Local Smoothing Estimates for Fourier Integral Operators
Sharp Local Smoothing Estimates for Fourier Integral Operators
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DOI：
10.1007/978-3-030-72058-2_2
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
David Beltran;J. Hickman;C. Sogge
中科院分区：
文献类型：
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作者：
David Beltran;J. Hickman;C. Sogge
本文综述了Fourier积分算子的理论，着重介绍了局部光滑估计及其应用。在回顾了经典背景之后，我们描述了作者最近的一些工作，建立了一类自然Fourier积分算子的局部光滑估计。我们还展示了如何本地平滑估计意味着振荡积分估计，并获得一个最大的变化的振荡积分估计斯坦。再加上布尔增益的振荡积分反例，这表明我们的局部平滑估计是尖锐的奇数空间维度。受相关反例的启发，我们制定了本地平滑的aptures考虑到自然的几何假设所产生的结构的傅立叶积分。
The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local smoothing estimates for a natural class of Fourier integral operators. We also show how local smoothing estimates imply oscillatory integral estimates and obtain a maximal variant of an oscillatory integral estimate of Stein. Together with an oscillatory integral counterexample of Bourgain, this shows that our local smoothing estimates are sharp in odd spatial dimensions. Motivated by related counterexamples, we formulate local smoothing conjectures which take into account natural geometric assumptions arising from the structure of the Fourier integrals.