Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal Function Characterizations of Hardy Spaces Associated to
  Homogeneous Higher Order Elliptic Operators   Let $L$ be a homogeneous divergence form higher order elliptic operator with
complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the maximal
interval of exponents $q\in[1,\,\infty]$ such that the semigroup
$\{e^{-tL}\}_{t>0}$ is bounded on $L^q(\mathbb{R}^n)$. In this article, the
authors establish the non-tangential maximal function characterizations of the
associated Hardy spaces $H_L^p(\mathbb{R}^n)$ for all $p\in(0,\,p_+(L))$,
which, when $p=1$, answers a question asked by Deng et al. in [J. Funct. Anal.
263 (2012), 604-674]. Moreover, the authors characterize $H_L^p(\mathbb{R}^n)$
via various versions of square functions and Lusin-area functions associated to
the operator $L$.

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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: eess