# Maximal subspace averages

@inproceedings{Plinio2021MaximalSA, title={Maximal subspace averages}, author={Francesco Di Plinio and Ioannis Parissis}, year={2021} }

We study maximal operators associated to singular averages along finite subsets Σ of the Grassmannian Gr(3,=) of 3-dimensional subspaces of R . The well studied 3 = 1 case corresponds to the the directional maximal function with respect to arbitrary finite subsets of Gr(1, =) = S=−1. We provide a systematic study of all cases 1 ≤ 3 < = and prove essentially sharp ! (R=) bounds for the maximal subspace averaging operator in terms of the cardinality of Σ, with no assumption on the structure of… Expand

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