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arXiv · 1612.03028

Positive sparse domination of variational Carleson operators

Francesco Di Plinio·Yen Q. Do·Gennady N. Uraltsev
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Abstract

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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Francesco Di Plinio, Yen Q. Do, Gennady N. Uraltsev. 2016-12-09. Positive sparse domination of variational Carleson operators. https://arxiv.org/abs/1612.03028

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