Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of sharp inequalities on real spheres   We prove a family of sharp multilinear integral inequalities on real spheres
involving functions that possess some symmetries that can be described by
annihilation by certain sets of vector fields. The Lebesgue exponents involved
are seen to be related to the combinatorics of such sets of vector fields.
Moreover we derive some Euclidean Brascamp--Lieb inequalities localized to a
ball of radius $R$, with a blow-up factor of type $R^\delta$, where the
exponent $\delta>0$ is related to the aforementioned Lebesgue exponents, and
prove that in some cases $\delta$ is optimal.

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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th