Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Littlewood-Paley Characterizations of Hardy-type Spaces Associated with
  Ball Quasi-Banach Function Spaces   Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this
article, assuming that the powered Hardy--Littlewood maximal operator satisfies
some Fefferman--Stein vector-valued maximal inequality on $X$ and is bounded on
the associated space, the authors establish various Littlewood--Paley function
characterizations of the Hardy space $H_X({\mathbb R}^n)$ associated with $X$,
under some weak assumptions on the Littlewood--Paley functions. To this end,
the authors also establish a useful estimate on the change of angles in tent
spaces associated with $X$. All these results have wide applications.
Particularly, when $X:=M_r^p({\mathbb R}^n)$ (the Morrey space),
$X:=L^{\vec{p}}({\mathbb R}^n)$ (the mixed-norm Lebesgue space),
$X:=L^{p(\cdot)}({\mathbb R}^n)$ (the variable Lebesgue space),
$X:=L_\omega^p({\mathbb R}^n)$ (the weighted Lebesgue space) and
$X:=(E_\Phi^r)_t({\mathbb R}^n)$ (the Orlicz-slice space), the
Littlewood--Paley function characterizations of $H_X({\mathbb R}^n)$ obtained
in this article improve the existing results via weakening the assumptions on
the Littlewood--Paley functions and widening the range of $\lambda$ in the
Littlewood--Paley $g_\lambda^*$-function characterization of $H_X(\mathbb
R^n)$.

9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph