New bounds for Kakeya problems
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We establish new estimates on the Minkowski and Hausdorff dimensions of Kakeya sets and we obtain new bounds on the Kakeya maximal operator.
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- J. Bourgain,Harmonic analysis and combinatorics: How much may they contribute to each other? inMathematics: Frontiers and Perspectives, IMU/Amer. Math. Soc. Providence, RI, 2000, pp. 13–32.Google Scholar
- I. łaba and T. Tao,An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension, Geom. Funct. Anal., to appear.Google Scholar
- D. Müller,On weighted estimates for the Kakeya operator, Colloq. Math.60/61 (1990), 457–475.Google Scholar
- I. Ruzsa,Sums of finite sets, inNumber Theory: New York Seminar (D. V. Chudnovsky, G. V. Chudnovsky and M. B. Nathanson, eds.), Springer-Verlag, Berlin, 1996.Google Scholar
- T. Wolff,Recent work connected with the Kakeya problem, inProspects in Mathematics (Princeton, NJ, 1996), Amer. Math. Soc., Providence, RI, 1999, pp. 129–162.Google Scholar
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