Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Composition operators on Sobolev spaces and weighted moduli inequalities   In this paper we study connections between composition operators on Sobolev
spaces and mappings defined by $p$-moduli inequalities ($p$-capacity
inequalities). We prove that weighted moduli inequalities lead to composition
operators on corresponding Sobolev spaces and inverse, composition operators on
Sobolev spaces imply weighted moduli inequalities.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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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-th
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The categories of this paper are: eess
10
The categories of this paper are: q-bio