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arXiv · 1802.04312

A restriction estimate in $\mathbb{R}^3$ using brooms

Hong Wang
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Abstract

If $f$ is a function supported on the truncated paraboloid in $\mathbb{R}^3$ and $E$ is the corresponding extension operator, then we prove that for all $p> 3+ 3/13$, $\|Ef\|_{L^p(\mathbb{R}^3)}\leq C \|f\|_{L^{\infty}}$. The proof combines Wolff's two ends argument with polynomial partitioning techniques. We also observe some geometric structures in wave packets.

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Hong Wang. 2018-02-12. A restriction estimate in $\mathbb{R}^3$ using brooms. https://arxiv.org/abs/1802.04312

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