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arXiv · 2507.22695

Local smoothing and maximal estimates for average over surfaces of codimension 2 in $\mathbb R^4$

Seheon Ham·Hyerim Ko
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Abstract

In this paper, we obtain local smoothing estimates for the averages over nondegenerate surfaces of codimension $2$ in $\mathbb R^4$. We make use of multilinear restriction estimates and decoupling inequalities for a hypersurface in $\mathbb R^5$, a conical extension of a two-dimensional nondegenerate surface along two flat directions. We also establish sharp $L^p$--$L^q$ estimates for maximal averages over nondegenerate surfaces of half the ambient dimension in $\mathbb R^{2n}$ for even $n \ge 2$.

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Seheon Ham, Hyerim Ko. 2025-07-30. Local smoothing and maximal estimates for average over surfaces of codimension 2 in $\mathbb R^4$. https://arxiv.org/abs/2507.22695

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