Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherical reflection positivity and the Hardy-Littlewood-Sobolev
  inequality   We introduce the concept of spherical (as distinguished from planar)
reflection positivity and use it to obtain a new proof of the sharp constants
in certain cases of the HLS and the logarithmic HLS inequality. Our proofs
relies on an extension of a work by Li and Zhu which characterizes the
minimizing functions of the type $(1+|x|^2)^{-p}$.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: solv-int