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Caltech/UCLA Joint Analysis Seminar

Friday, October 19, 2018
5:00pm to 5:45pm
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Linde Hall 310
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.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].