Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev spaces on graded groups   We study the Lp-properties of positive Rockland operators and define Sobolev
spaces on general graded groups. This generalises the case of sub-Laplacians on
stratified groups studied by G. Folland in [3]. We show that the defined
Sobolev spaces are actually independent of the choice of a positive Rockland
operator. Furthermore, we show that they are interpolation spaces and establish
duality and Sobolev embedding theorems in this context.

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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph