Positive sparse domination of variational Carleson operators

2016/12/09 by Di Plinio, Francesco, Do, Yen Q., Uraltsev, Gennady N. · 1 citation
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.03028

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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