Kakeya Sets and Directional Maximal Operators in the Plane

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dc.creatorBateman, Michael
dc.date2007-03-19
dc.date.accessioned2026-07-07T07:52:39Z
dc.date.available2026-07-07T07:52:39Z
dc.descriptionWe completely characterize the boundedness of planar directional maximal operators on L^p. More precisely, if Omega is a set of directions, we show that M_Omega, the maximal operator associated to line segments in the directions Omega, is unbounded on L^p, for all p < infinity, precisely when Omega admits Kakeya-type sets. In fact, we show that if Omega does not admit Kakeya sets, then Omega is a generalized lacunary set, and hence M_Omega is bounded on L^p, for p>1.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0703559
dc.identifierhttp://arxiv.org/abs/math/0703559
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125954
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.subjectProbability
dc.subject42B25, 60K35
dc.titleKakeya Sets and Directional Maximal Operators in the Plane
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