奇异积分满足调制不变性
Singular integrals meet modulation invariance
摘要：
欧几里得空间上的傅里叶分析的许多概念依赖于频率点的指定。例如，经典的Littlewood Paley理论将函数谱分解为以原点为中心的环。在光谱平移（调制）下不变的结构的存在下，这些概念需要细化。这是由L首先完成的。Carleson在他的证明几乎处处收敛的傅里叶级数于1966年。M的工作。Lacey和作者在20世纪90年代关于双线性希尔伯特变换，一个调制不变奇异积分的原型，使这一主题重新活跃起来。它现在是一个活跃的研究课题，将在讲座中进行调查。作者最近的相关工作大部分是与C. Muscalu和T.涛.
英文摘要：
Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of structures which are invariant under translation of the spectrum (modulation) these concepts need to be refined. This was first done by L. Carleson in his proof of almost everywhere convergence of Fourier series in 1966. The work of M. Lacey and the author in the 1990's on the bilinear Hilbert transform, a prototype of a modulation invariant singular integral, has revitalized the theme. It is now subject of active research which will be surveyed in the lecture. Most of the recent related work by the author is joint with C. Muscalu and T. Tao.
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