Heisenberg Hausdorff Dimension of Besicovitch Sets

• Autorzy: Laura Venieri
• Języki publikacji: EN

Abstrakty

EN

We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.

Słowa kluczowe

EN

Besicovitch set; Kakeya maximal function; Heisenberg group; Hausdorff dimension

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-06-06

zaakceptowano

2014-11-03

online

2014-11-28

Twórcy

autor

Laura Venieri

• Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin katu 2b),
  FI-00014 University of Helsinki, Finland

Bibliografia

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• [2] J. Bourgain. On the dimension of Kakeya sets and related maximal inequalities. Geom. Funct. Anal., 9(2):256–282, 1999.
• [3] Roy O. Davies. Some remarks on the Kakeya problem. Mathematical Proceedings of the Cambridge Philosophical Society, 69:417–421, 5 1971.
• [4] Nets Hawk Katz and Terence Tao. Bounds on arithmetic projections, and applications to the Kakeya conjecture. Math. Res. Lett., 6(5-6):625–630, 1999.
• [5] Nets Hawk Katz and Terence Tao. New bounds for Kakeya problems. J. Anal. Math., 87:231–263, 2002. Dedicated to the memory of Thomas H. Wolff.
• [6] Pertti Mattila. Fourier transform and Hausdorff dimension. http://wiki.helsinki.fi/display/mathstatKurssit/Fourier+ transform+and+Hausdorff+dimension%2C+spring+2014.
• [7] Terence Tao. The Bochner-Riesz conjecture implies the restriction conjecture. Duke Math. J., 96(2):363–375, 1999.
• [8] Thomas Wolff. An improved bound for Kakeya type maximal functions. Rev. Mat. Iberoamericana, 11(3):651–674, 1995.

Identyfikatory

DOI

10.2478/agms-2014-0013