Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decoupling and near-optimal restriction estimates for Cantor sets   For any $\alpha\in(0,d)$, we construct Cantor sets in $\mathbb{R}^d$ of
Hausdorff dimension $\alpha$ such that the associated natural measure $\mu$
obeys the restriction estimate $\| \widehat{f d\mu} \|_{p} \leq C_p \| f
\|_{L^2(\mu)}$ for all $p>2d/\alpha$. This range is optimal except for the
endpoint. This extends the earlier work of Chen-Seeger and Shmerkin-Suomala,
where a similar result was obtained by different methods for $\alpha=d/k$ with
$k\in\mathbb{N}$. Our proof is based on the decoupling techniques of
Bourgain-Demeter and a theorem of Bourgain on the existence of $\Lambda(p)$
sets.

18
The categories of this paper are: econ
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
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The categories of this paper are: funct-an