Small cap decouplings

@article{Demeter2019SmallCD,
  title={Small cap decouplings},
  author={C. Demeter and L. Guth and H. Wang},
  journal={arXiv: Classical Analysis and ODEs},
  year={2019}
}
We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in $\mathbb{R}^3$. This part of the work relies on recent improved Kakeya-type estimates for planar tubes, as well as on new… Expand

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