Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Adams type inequalities in Sobolev spaces
  $W^{m,\frac{n}{m}}(\mathbb{R}^{n})$ for arbitrary integer $m$   The main purpose of our paper is to prove sharp Adams-type inequalities in
unbounded domains of $\mathbb{R}^{n}$ for the Sobolev space
$W^{m,\frac{n}{m}}\left(\mathbb{R} ^{n}\right)$ for any positive integer $m$
less than $n$. Our results complement those of Ruf and Sani \cite{RS} where
such inequalities are only established for even integer $m$. Our inequalities
are also a generalization of the Adams-type inequalities in the special case
$n=2m=4$ proved in \cite{Y} and stronger than those in \cite{RS} when $n=2m$
for all positive integer $m$ by using different Sobolev norms.

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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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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: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: q-bio