Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A derivation of the sharp Moser-Trudinger-Onofri inequalities from the
  fractional Sobolev inequalities   We derive the sharp Moser-Trudinger-Onofri inequalities on the standard
$n$-sphere and CR $(2n+1)$- sphere as the limit of the sharp fractional Sobolev
inequalities for all $n\ge 1$. On the $2$-sphere and $4$-sphere, this was
established recently by S.-Y. Chang and F. Wang. Our proof uses an alternative
and elementary argument.

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The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio