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Friday, October 19, 2018
5:00 PM - 5:45 PM
Linde Hall 310

Caltech/UCLA Joint Analysis Seminar

A restriction estimate in $\mathbb{R}^3$
Hong Wang, Department of Mathematics, MIT,

If f is a function supported on a truncated paraboloid, what can we say about Ef, the Fourier transform of f? Stein conjectured in the 1960s that for any p>3, $\|Ef\|_{L^p(R^3)} \lesssim \|f\|_{L^{\infty}}$.

We make a small progress toward this conjecture and show that p> 3+3/13\approx 3.23. In the proof, we combine polynomial partitioning techniques introduced by Guth and the two ends argument introduced by Wolff and Tao.

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