Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilinear identities involving the $k$-plane transform and Fourier
  extension operators   We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension
operators associated to spheres and hyperboloids under the action of the
$k$-plane transform. As the estimates are $L^2$-based, they follow from
bilinear identities: in particular, these are the analogues of a known identity
for paraboloids, and may be seen as higher-dimensional versions of the
classical $L^2(\mathbb{R}^2)$-bilinear identity for Fourier extension operators
associated to curves in $\mathbb{R}^2$.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex