L^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2

dc.creatorBateman, Michael
dc.date2008-02-01
dc.date.accessioned2026-07-07T09:18:17Z
dc.date.available2026-07-07T09:18:17Z
dc.descriptionWe 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.description10 pages
dc.identifierhttps://arxiv.org/abs/0802.0183
dc.identifierhttp://arxiv.org/abs/0802.0183
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153969
dc.subjectClassical Analysis and ODEs
dc.subject42B25
dc.titleL^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2
dc.typetext

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