Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces   Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on
$\mathbb{R}^n$. Let $H^{p,q}_A(\mathbb{R}^n)$ be the anisotropic Hardy-Lorentz
spaces associated with $A$ defined via the non-tangential grand maximal
function. In this article, the authors characterize $H^{p,q}_A(\mathbb{R}^n)$
in terms of the Lusin-area function, the Littlewood-Paley $g$-function or the
Littlewood-Paley $g_\lambda^*$-function via first establishing an anisotropic
Fefferman-Stein vector-valued inequality in the Lorentz space
$L^{p,q}(\mathbb{R}^n)$. All these characterizations are new even for the
classical isotropic Hardy-Lorentz spaces on $\mathbb{R}^n$. Moreover, the range
of $\lambda$ in the $g_\lambda^*$-function characterization of
$H^{p,q}_A(\mathbb{R}^n)$ coincides with the best known one in the classical
Hardy space $H^p(\mathbb{R}^n)$ or in the anisotropic Hardy space
$H^p_A(\mathbb{R}^n)$.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga