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arXiv · 2404.17748

Sharp $\ell^q(L^p)$ decoupling for paraboloids

Tongou Yang
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Abstract

In this short expository note, we prove the following result, which is a special case of the main theorem in arXiv:2011.09451. For each $n \ge 2$ and $p, q \in [2, \infty]$, we prove upper bounds of $\ell^q(L^p)$ decoupling constants for paraboloids in $\mathbb R^n$, as well as presenting extremisers for each case. Both are sharp up to $\varepsilon$-losses.

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Tongou Yang. 2024-04-27. Sharp $\ell^q(L^p)$ decoupling for paraboloids. https://arxiv.org/abs/2404.17748

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