L^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2
| dc.creator | Bateman, Michael | |
| dc.date | 2008-02-01 | |
| dc.date.accessioned | 2026-07-07T09:18:17Z | |
| dc.date.available | 2026-07-07T09:18:17Z | |
| dc.description | We prove a conjecture of Lacey and Li in the case that the vector field depends only on one variable. Specifically: let v be a vector field defined on the unit square such that v(x,y) = (1,u(x)) for some measurable u from [0,1] to [0,1]. Fix a small parameter delta and let Z be the collection of rectangles R of a fixed width such that delta much of the vector field inside R is pointed in (approximately) the same direction as R. We show that the maximal averaging operator associated to the collection Z is bounded on L^p for p>1 with constants comparable to (delta)^(-1) . | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0183 | |
| dc.identifier | http://arxiv.org/abs/0802.0183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153969 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B25 | |
| dc.title | L^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2 | |
| dc.type | text |