Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Poincare and logarithmic Sobolev inequalities for measure
  spaces   We prove generalizations of the Poincare and logarithmic Sobolev inequalities
corresponding to the case of fractional derivatives in measure spaces with only
a minimal amount of geometric structure. The class of such spaces includes (but
is not limited to) spaces of homogeneous type with doubling measures. Several
examples and applications are given, including Poincare inequalities for graph
Laplacians, Fractional Poincare inequalities of Mouhot, Russ, and Sire [16],
and implications for recent work of the author and R. M. Strain on the
Boltzmann collision operator [10, 11, 9].

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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys