Real Analysis Exchange

Norm Estimates for the Kakeya Maximal Function with Respect to General Measures

Themis Mitsis

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We generalize Bourgain's theorem on the two dimensional Kakeya maximal function by proving norm estimates with respect to measures satisfying certain conditions. We use this to extend the classical result of Davies on the Hausdorff dimension of Kakeya sets in the plane.

Article information

Real Anal. Exchange, Volume 27, Number 2 (2001), 563-572.

First available in Project Euclid: 2 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory 28A78: Hausdorff and packing measures

Kakeya maximal function Hausdorff measures


Mitsis, Themis. Norm Estimates for the Kakeya Maximal Function with Respect to General Measures. Real Anal. Exchange 27 (2001), no. 2, 563--572.

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