Bounds for Kakeya-type maximal operators associated with k-planes
| dc.creator | Oberlin, Richard | |
| dc.date | 2005-12-15 | |
| dc.date.accessioned | 2026-07-07T06:55:23Z | |
| dc.date.available | 2026-07-07T06:55:23Z | |
| dc.description | A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for k \geq k_{cr}(d), where k_{cr}(d) solves 2^{k_{cr}-1}+k_{cr} = d, every (d,k) set has positive Lebesgue measure. We give a short proof of this result which allows for an improved L^p estimate of the corresponding maximal operator, and which demonstrates that a lower value of k_{cr} could be obtained if improved mixed-norm estimates for the x-ray transform were known. | |
| dc.description | 9 pages. No figures | |
| dc.identifier | https://arxiv.org/abs/math/0512377 | |
| dc.identifier | http://arxiv.org/abs/math/0512377 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106260 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B25 | |
| dc.title | Bounds for Kakeya-type maximal operators associated with k-planes | |
| dc.type | text |