Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pitt's inequality with sharp convolution estimates   Sharp $L^p$ extensions of Pitt's inequality expressed as a weighted Sobolev
inequality are obtained using convolution estimates and Stein-Weiss potentials.
More generally, optimal constants are obtained for the full Stein-Weiss
potential as a map from $L^p$ to itself, and new proofs are given for the
classical Pitt and Stein-Weiss estimates.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics