Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp affine weighted $L^p$ Sobolev type inequalities   We establish sharp affine weighted $L^p$ Sobolev type inequalities by using
the $L_p$ Busemann-Petty centroid inequality proved by Lutwak, Yang and Zhang.
Our approach consists in combining in a convenient way the latter one with a
suitable family of sharp weighted $L^p$ Sobolev type inequalities obtained by
Nguyen and allows to characterize all extremizers in some cases. The new
inequalities don't rely on any euclidean geometric structure.

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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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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: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex