Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interpolation between $H^{p(\cdot)}(\mathbb R^n)$ and $L^\infty(\mathbb
  R^n)$: Real Method   Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function
satisfying the globally log-H\"older continuous condition. In this article, the
authors first obtain a decomposition for any distribution of the variable weak
Hardy space into "good" and "bad" parts and then prove the following real
interpolation theorem between the variable Hardy space $H^{p(\cdot)}(\mathbb
R^n)$ and the space $L^{\infty}(\mathbb R^n)$: \begin{equation*}
(H^{p(\cdot)}(\mathbb R^n),L^{\infty}(\mathbb R^n))_{\theta,\infty}
=W\!H^{p(\cdot)/(1-\theta)}(\mathbb R^n),\quad \theta\in(0,1), \end{equation*}
where $W\!H^{p(\cdot)/(1-\theta)}(\mathbb R^n)$ denotes the variable weak Hardy
space. As an application, the variable weak Hardy space
$W\!H^{p(\cdot)}(\mathbb R^n)$ with
$p_-:=\mathop\mathrm{ess\,inf}_{x\in\rn}p(x)\in(1,\infty)$ is proved to
coincide with the variable Lebesgue space $W\!L^{p(\cdot)}(\mathbb R^n)$.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin