Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A restriction estimate in $\mathbb{R}^3$ using brooms   If $f$ is a function supported on the truncated paraboloid in $\mathbb{R}^3$
and $E$ is the corresponding extension operator, then we prove that for all $p>
3+ 3/13$, $\|Ef\|_{L^p(\mathbb{R}^3)}\leq C \|f\|_{L^{\infty}}$. The proof
combines Wolff's two ends argument with polynomial partitioning techniques. We
also observe some geometric structures in wave packets.

31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas