Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted norm inequalities for the maximal operator on $\Lpp$ over
  spaces of homogeneous type   Given a space of homogeneous type $(X,\mu,d)$, we prove strong-type weighted
norm inequalities for the Hardy-Littlewood maximal operator over the variable
exponent Lebesgue spaces $L^\pp$. We prove that the variable Muckenhoupt
condition $\App$ is necessary and sufficient for the strong type inequality if
$\pp$ satisfies log-H\"older continuity conditions and $1 < p_- \leq p_+ <
\infty$. Our results generalize to spaces of homogeneous type the analogous
results in Euclidean space proved by Cruz-Uribe, Fiorenza and Neugebuaer
(2012).

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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th