Kakeya sets and directional maximal operators in the plane

By M. Bateman. 2007

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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 1.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52ad573d43fe5a1a0d692141a14d2dadc8f1a574