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Oscillatory integrals in Fourier analysis. (English) Zbl 0618.42006
Beijing lectures in harmonic analysis, Ann. Math. Stud. 112, 307-355 (1986).
[For the entire collection see Zbl 0595.00015.]
This lecture is a survey and some new results on oscillatory integrals are also given. Starting with some basic theorems the author discusses the Fourier transforms of measures with support in a smooth surface in \({\mathbb{R}}^ n\), the restriction to a surface of Fourier transforms of functions in \(L^ p({\mathbb{R}}^ n)\), the oscillatory integrals arising in the theory of Hilbert transform along curves, and those suggested by twisted convolution on the Heisenberg group and the theory of Radon singular integrals. The lecture is very instructive and enjoyable to read.
Reviewer: H.Tanabe

MSC:
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)