Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp superlevel set estimates for small cap decouplings of the parabola   We prove sharp bounds for the size of superlevel sets $\{x\in
\mathbb{R}^2:|f(x)|>\alpha\}$ where $\alpha>0$ and
$f:\mathbb{R}^2\to\mathbb{C}$ is a Schwartz function with Fourier transform
supported in an $R^{-1}$-neighborhood of the truncated parabola $\mathbb{P}^1$.
These estimates imply the small cap decoupling theorem for $\mathbb{P}^1$ of
Demeter, Guth, and Wang, and the canonical decoupling theorem for
$\mathbb{P}^1$ of Bourgain and Demeter. New $(\ell^q,L^p)$ small cap decoupling
inequalities also follow from our sharp level set estimates.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: atom-ph