Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic Characterizations of Hardy Spaces Associated to Schr\"{o}dinger
  Type Operators   In this article, the authors consider the Schr\"{o}dinger type operator
$L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix
$A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative
potential $V$ belongs to the reverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with
$q\in(n/2,\,\infty)$. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$ be a variable
exponent function satisfying the globally $\log$-H\"{o}lder continuous
condition. The authors introduce the variable Hardy space
$H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$ and establish its atomic
characterization. The atoms here are closer to the atoms of variable Hardy
space $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit, which further implies that
$H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in
$H_L^{p(\cdot)}(\mathbb{R}^n)$.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph