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arXiv · 2603.07934

A note on small cap square function and decoupling estimates for the parabola

Jongchon Kim·Liang Wang·Chun Keung Yeung
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Abstract

In this paper, we prove small cap square function and decoupling estimates for the parabola, where the small caps are essentially axis-parallel rectangles of dimensions $\delta\times \delta^\beta$ for $0\leq \beta\leq 1$. Our estimates complement the known results for $1 \leq \beta \leq 2$ and are sharp up to polylogarithmic factors.

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Jongchon Kim, Liang Wang, Chun Keung Yeung. 2026-03-09. A note on small cap square function and decoupling estimates for the parabola. https://arxiv.org/abs/2603.07934

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