Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere   We prove sharp inequalities of Hardy type for functions in the Sobolev space
$W^{1,p}$ on the unit sphere $\mathbb{S}^{n-1}$ in $\mathbb{R}^{n}$. We achieve
this in both the subcritical and critical cases. The method we use to show
optimality takes into account all the constants involved in our inequalities.

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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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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: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc