Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third Version of Weak Orlicz--Morrey Spaces and Its Inclusion Properties   Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces
which were first introduced by Nakai. There are three versions of
Orlicz--Morrey spaces, i.e: Nakai's (2004), Sawano--Sugano--Tanaka's (2012),
and Deringoz--Guliyev--Samko's (2014) versions. On this article we will discuss
the third version of weak Orlicz--Morrey space which is seen as an enlargement
of third version of (strong) Orlicz--Morrey space. Similar to its first version
and second version, the third version of weak Orlicz-Morrey space is considered
as a generalization of weak Orlicz spaces, weak Morrey spaces, and generalized
weak Morrey spaces. In this study, we will investigate some properties of the
third version of weak Orlicz--Morrey spaces, especially the sufficient and
necessary conditions for inclusion relations between two these spaces. One of
the keys to get our result is to estimate the quasi-norm of characteristics
function of open balls in $\mathbb{R}^n$.

20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin