Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a weighted variable spaces $L_{p(x), \omega}$ for $0< p(x)< 1$ and
  weighted Hardy inequality   In this paper a weighted variable exponent Lebesgue spaces $L_{p(x), \omega}$
for $0< p(x)< 1$ is investigated. We show that this spaces is a quasi-Banach
spaces. Note that embedding theorem between weight variable Lebesgue spaces is
proved. In particular, we show that $L_{p(x), \omega}(\Omega)$ for $0< p(x)< 1$
isn't locally convex. Also, in this paper a some two-weight estimates for Hardy
operator are proved.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs