The Proof of restriction conjecture In $\mathbb{R}^{3}$

Hoyoung Song

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arXiv · 2304.01092

The Proof of restriction conjecture In $\mathbb{R}^{3}$

Hoyoung Song

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Abstract

If S is a smooth compact surface in $\mathbb{R}^{3}$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3$, $\left\|E_S f\right\|_{L^p\left(\mathbb{R}^3\right)} \leq C(p, S)\|f\|_{L^{\infty}(S)}.$ The proof of restriction conjecture in $\mathbb{R}^{3}$ implies that Kakeya set conjecture is true when n=3.

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Hoyoung Song. 2023-04-03. The Proof of restriction conjecture In $\mathbb{R}^{3}$. https://arxiv.org/abs/2304.01092

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