English

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

Classical Analysis and ODEs 2026-03-10 v1

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 δ×δβ\delta\times \delta^\beta for 0β10\leq \beta\leq 1. Our estimates complement the known results for 1β21 \leq \beta \leq 2 and are sharp up to polylogarithmic factors.

Cite

@article{arxiv.2603.07934,
  title  = {A note on small cap square function and decoupling estimates for the parabola},
  author = {Jongchon Kim and Liang Wang and Chun Keung Yeung},
  journal= {arXiv preprint arXiv:2603.07934},
  year   = {2026}
}

Comments

15 pages

R2 v1 2026-07-01T11:09:37.403Z