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arXiv · 2503.14276

On decoupling and restriction estimates

Changkeun Oh
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Abstract

In this short note, we prove that the restriction conjecture for the (hyperbolic) paraboloid in $\mathbb{R}^d$ implies the $l^p$-decoupling theorem for the (hyperbolic) paraboloid in $\mathbb{R}^{2d-1}$. In particular, this gives a simple proof of the $l^p$ decoupling theorem for the (hyperbolic) paraboloid in $\mathbb{R}^3$.

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Changkeun Oh. 2025-03-18. On decoupling and restriction estimates. https://doi.org/10.1017/s030500412510145x

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