Abstract
We develop almost-orthogonality principles for maximal functions associated with averages over line segments and directional singular integrals. Using them, we obtain sharp L2-bounds for these maximal functions when the underlying direction set is equidistributed in Sn-1.
| Original language | English |
|---|---|
| Pages (from-to) | 7320-7332 |
| Number of pages | 13 |
| Journal | Journal of Geometric Analysis |
| Volume | 31 |
| Issue number | 7 |
| Online published | 20 Aug 2020 |
| DOIs | |
| Publication status | Published - Jul 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2020, Mathematica Josephina, Inc.
Funding
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.
Research Keywords
- Almost-orthogonality principle
- Directional maximal function
- Directional singular integral
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