Kakeya Sets in Cantor directions
| dc.creator | Bateman, Michael D. | |
| dc.creator | Katz, Nets Hawk | |
| dc.date | 2006-09-06 | |
| dc.date.accessioned | 2026-07-07T07:24:35Z | |
| dc.date.available | 2026-07-07T07:24:35Z | |
| dc.description | We construct a union of N parallelograms of dimensions approximately 1/N x 1 in the plane, with the slope of their long sides in the standard Cantor set. The union has area 1/log N but the union of the doubles has area log log N/ log N. In particular, this implies unbounded of the associated maximal operator in L^p for any p different from infinity. The construction is by randomizing an earlier construction of the second author for the L^2 case. The proof that the construction satisfies the desired conditions is by elementary estimates in the theory of percolation on trees as developed by R. Lyons. | |
| dc.description | 10 pages; Preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0609187 | |
| dc.identifier | http://arxiv.org/abs/math/0609187 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116411 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 42B25,60K35 | |
| dc.title | Kakeya Sets in Cantor directions | |
| dc.type | text |