Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted Inequalities for the Fractional Laplacian and the Existence of
  Extremals   In this article we obtain improved versions of Stein-Weiss and
Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative
smoothness. As an application of the former, we derive the existence of
extremals of the Stein-Weiss inequality in certain cases, some of which are not
contained in the celebrated theorem of E. Lieb.

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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an