Kakeya Sets and Directional Maximal Operators in the Plane

Details Kakeya Sets and Directional Maximal Operators in the Plane Kakeya Sets and Directional Maximal Operators in the Plane

2007-03-19

arxiv.org/abs/math/0703559v1

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

We 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.

Affiliated with

Also associated with

No associations

Rating

Kakeya Sets and Directional Maximal Operators in the Plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Kakeya Sets and Directional Maximal Operators in the Plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kakeya Sets and Directional Maximal Operators in the Plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31780