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»ã±¨ÌáÒª£º This talk is concerned with a topic in harmonic analysis. The Fourier restriction conjecture originated in Elias Stein's question in the late 60's. Stein asks whether it makes sense to restrict Fourier transforms of a function to a hypersurface in the n dimensional Euclidean spaces such as the sphere, the paraboloids, or the cone. Equivalently it concerns establishing strong type Lebesgue space estimates for Fourier transforms of certain surface carried measures. Such are called Fourier restriction estimates. They are connected to Strichartz's estimates in partial differential equations. In this talk we will discuss some ``recent" progress towards this problem. More precisely we will report Tao's paper in 2003 to illustrate a central idea used in recent proofs. The proof establishes a bilinear restriction estimate for paraboloids by using Wolff's induction on scales.

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