Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Marcinkiewicz integral type characterization of the Sobolev space   In this paper we present a new characterization of the Sobolev space
$W^{1,p}$, $1<p<\infty$ which is a higher dimensional version of a result of
Waterman. We also provide a new and simplified proof of a recent result of
Alabern, Mateu and Verdera. Finally, we generalize the results to the case of
weighted Sobolev spaces with respect to a Muckenhoupt weight.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
19
The categories of this paper are: eess