Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several analytic inequalities in some $Q-$spaces   In this paper, we establish separate necessary and sufficient
  John-Nirenberg (JN) type inequalities for functions in
  $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ which imply Gagliardo-Nirenberg (GN)
type inequalities in
  $Q_{\alpha}(\mathbb{R}^{n}).$ Consequently, we obtain Trudinger-Moser type
inequalities and Brezis-Gallouet-Wainger type inequalities in
$Q_{\alpha}(\mathbb{R}^{n}).$

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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin