Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hausdorff operators on the Sobolev spaces $W^{k,1}$   This paper is served as a first contribution regarding the boundedness of
Hausdorff operators on function spaces with smoothness. The sharp conditions
are established for boundedness of Hausdorff operators on Sobolev spaces
$W^{k,1}$. As applications, some bounded and unbounded properties of Hardy
operator and adjoint Hardy operator on $W^{k,1}$ are deduced.

4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph