|
|||||
 |
|
|
|
|
|
|
|
An $L^{3/2}$
$\mathrm{SL}_2$ Kakeya maximal inequality
John Green, Terence L. J. Harris and Yumeng Ou |
|
Vol. 19 (2026), No. 7, 1295–1338
|
 |
Abstract |
|
We prove a special case of the Kakeya maximal function conjecture in , with loss, when the centre lines of the tubes are lines and the tubes satisfy a 2-dimensional ball condition (equivalent to the Wolff axioms in this case). We show that the exponent is sharp and that some loss (such as ) is necessary, even in the case where the -tubes have -separated directions and the cardinality of the tube family is maximal (). The Kakeya maximal inequality is deduced from an inequality for restricted families of projections onto planes. A related inequality is also derived for restricted projections onto lines, and an application is given to generic intersections of sets in with “light rays” and “light planes”. |
Keywords
Besicovitch set, Kakeya maximal function, restricted
projections
|
Mathematical Subject Classification
Primary: 28A78, 28A80
|
Milestones
Received: 21 June 2024
Revised: 6 May 2025
Accepted: 19 September 2025
Published: 18 September 2026
|
Authors |
| John Green | |
| Mathematics Institute University of Warwick Coventry United Kingdom |
|
| Terence L. J. Harris | |
| Department of Mathematics University of Wisconsin-Madison Madison, WI United States |
|
| Yumeng Ou | |
| Department of Mathematics University of Pennsylvania Philadelphia, PA United States |
|
| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
