Heisenberg Hausdorff Dimension of Besicovitch Sets
Analysis and Geometry in Metric Spaces (2014)
- Volume: 2, Issue: 1, page 319-327, electronic only
- ISSN: 2299-3274
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Abstract
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topLaura Venieri. "Heisenberg Hausdorff Dimension of Besicovitch Sets." Analysis and Geometry in Metric Spaces 2.1 (2014): 319-327, electronic only. <http://eudml.org/doc/268882>.
@article{LauraVenieri2014,
abstract = {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.},
author = {Laura Venieri},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Besicovitch set; Kakeya maximal function; Heisenberg group; Hausdorff dimension},
language = {eng},
number = {1},
pages = {319-327, electronic only},
title = {Heisenberg Hausdorff Dimension of Besicovitch Sets},
url = {http://eudml.org/doc/268882},
volume = {2},
year = {2014},
}
TY - JOUR
AU - Laura Venieri
TI - Heisenberg Hausdorff Dimension of Besicovitch Sets
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 319
EP - 327, electronic only
AB - 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.
LA - eng
KW - Besicovitch set; Kakeya maximal function; Heisenberg group; Hausdorff dimension
UR - http://eudml.org/doc/268882
ER -
References
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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. Zbl0930.43005
- [3] Roy O. Davies. Some remarks on the Kakeya problem. Mathematical Proceedings of the Cambridge Philosophical Society, 69:417–421, 5 1971. Zbl0209.26602
- [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. Zbl1027.42014
- [6] Pertti Mattila. Fourier transform and Hausdorff dimension. http://wiki.helsinki.fi/display/mathstatKurssit/Fourier+ transform+and+Hausdorff+dimension%2C+spring+2014. Zbl1049.28007
- [7] Terence Tao. The Bochner-Riesz conjecture implies the restriction conjecture. Duke Math. J., 96(2):363–375, 1999. Zbl0980.42006
- [8] Thomas Wolff. An improved bound for Kakeya type maximal functions. Rev. Mat. Iberoamericana, 11(3):651–674, 1995. Zbl0848.42015
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