Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on generalized Poincar\'e-type inequalities with applications to
  weighted improved Poincar\'e-type inequalities   The main result of this paper supports a conjecture by C. P\'erez and E. Rela
about a very recent result of theirs on self-improving theory. Also, we extend
the conclusions of their theorem to the range $p<1$.
  As an application of our result, we give a unified vision of weighted
improved Poincar\'e-type inequalities in the Euclidean setting, which gathers
both weighted improved classical and fractional Poincar\'e inequalities within
an approach which avoids any representation formula. We improve some already
known results.
  Finally, we also explore analog inequalities in the context of metric spaces
by means of the already known self-improving results.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph