Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on
  $\mathbb{R}^n$ by Atoms and Molecules   Let $\vec{p}\in(0,\,\infty)^n$, $A$ be an expansive dilation on
$\mathbb{R}^n$,and $H^{\vec{p}}_A({\mathbb {R}}^n)$ be the anisotropic
mixed-norm Hardy space defined via the non-tangential grand maximal function
studied by \cite{hlyy20}. In this paper, the authors establish new atomic and
molecular decompositions of $H^{\vec{p}}_A({\mathbb {R}}^n)$. As an
application, the authors obtain a boundedness criterion for a class of linear
operators from $H^{\vec{p}}_{A}(\mathbb{R}^n)$ to
$H^{\vec{p}}_{A}(\mathbb{R}^n)$. Part of results are still new even in the
classical isotropic setting (in the case $A:=2\mathrm I_{n\times n}$,
${\mathrm{I}}_{n\times n}$ denotes the $n\times n$ unit matrix).

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics