Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates and structure of $\alpha$-harmonic functions   We prove a uniform boundary Harnack inequality for nonnegative harmonic
functions of the fractional Laplacian on arbitrary open set $D$. This yields a
unique representation of such functions as integrals against measures on
$D^c\cup \{\infty\}$ satisfying an integrability condition. The corresponding
Martin boundary of $D$ is a subset of the Euclidean boundary determined by an
integral test.

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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat