Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp total variation results for maximal functions   In this article, we prove some total variation inequalities for maximal
functions. Our results deal with two possible generalizations of the results
contained in Aldaz and P\'erez L\'azaro's work, one of whose considers a
variable truncation of the maximal function, and the other one interpolates the
centered and the uncentered maximal functions. In both contexts, we find sharp
constants for the desired inequalities, which can be viewed as progress towards
the conjecture that the best constant for the variation inequality in the
centered context is one. We also provide counterexamples showing that our
methods do not apply outside the stated parameter ranges.

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The categories of this paper are: econ
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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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: q-bio
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an