Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic weighted Sobolev-Poincar\'e type inequalities   We derive weighted Sobolev-Poincar\'e type inequalities in function spaces
concerned with parabolic partial differential equations. We consider general
weights depending on both space and time variables belonging to a Muckenhoupt
class, so-called the parabolic $A_p$-class, where only the parabolic cubes are
involved in the definition.

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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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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-ex
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con