215 citations
- Indiana University BloomingtonUS5 papers
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- Mitchell InstituteUS2 papers
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math.CA2007★ 3 cited
Kakeya Sets and Directional Maximal Operators in the Plane
Michael Bateman
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 operat…
math.CA2006★ 4 cited
Kakeya Sets in Cantor directions
Michael D. Bateman, Nets Hawk Katz
We construct a union of N parallelograms of dimensions approximately 1/N x 1 in the plane, with the slope of their long sides in the standard Cantor set. The union has area 1/log N…