Abstract
We develop almost-orthogonality principles for maximal functions associated with averages over line segments and directional singular integrals. Using them, we obtain sharp \(L^2\)-bounds for these maximal functions when the underlying direction set is equidistributed in \({\mathbb {S}}^{n-1}\).
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Acknowledgements
The author is partially supported by a PIMS Postdoctoral Fellowship and a Discovery grant from the Natural Sciences and Engineering Research Council of Canada. He thanks Malabika Pramanik for helpful discussions. He is grateful to the referees for their comments, which have improved the exposition of this paper.
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Kim, J. Almost-Orthogonality Principles for Certain Directional Maximal Functions. J Geom Anal 31, 7320–7332 (2021). https://doi.org/10.1007/s12220-020-00502-2
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DOI: https://doi.org/10.1007/s12220-020-00502-2