Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive sparse domination of variational Carleson operators   Due to its nonlocal nature, the $r$-variation norm Carleson operator $C_r$
does not yield to the sparse domination techniques of Lerner, Di Plinio and
Lerner, Lacey. We overcome this difficulty and prove that the dual form to
$C_r$ can be dominated by a positive sparse form involving $L^p$ averages. Our
result strengthens the $L^p$ estimates by Oberlin et. al. As a corollary, we
obtain quantitative weighted norm inequalities improving on previous results by
Do and Lacey. Our proof relies on the localized outer $L^p$-embeddings of Di
Plinio-Ou and Uraltsev.

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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph