# 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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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

top- [1] J. Bourgain. Besicovitch typemaximal operators and applications to Fourier analysis. Geom. Funct. Anal., 1(2):147–187, 1991. Zbl0756.42014
- [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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