Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Characterizations of Musielak-Orlicz-Sobolev Spaces via Sharp Ball
  Averaging Functions   In this article, the authors establish a new characterization of the
Musielak--Orlicz--Sobolev space on $\mathbb{R}^n$, which includes the classical
Orlicz--Sobolev space, the weighted Sobolev space and the variable exponent
Sobolev space as special cases, in terms of sharp ball averaging functions.
Even in a special case, namely, the variable exponent Sobolev space, the
obtained result in this article improves the corresponding result obtained by
P. H\"ast\"o and A. M. Ribeiro [Commun. Contemp. Math. 19 (2017), 1650022, 13
pp] via weakening the assumption $f\in L^1(\mathbb R^n)$ into $f\in
L_{\mathrm{loc}}^1(\mathbb R^n)$, which was conjectured to be true by H\"ast\"o
and Ribeiro in the aforementioned same article.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph