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.
@article{bwmeta1.element.doi-10_2478_agms-2014-0013,
author = {Laura Venieri},
title = {Heisenberg Hausdorff Dimension of Besicovitch Sets},
journal = {Analysis and Geometry in Metric Spaces},
volume = {2},
year = {2014},
zbl = {1303.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0013}
}
Laura Venieri. Heisenberg Hausdorff Dimension of Besicovitch Sets. Analysis and Geometry in Metric Spaces, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0013/
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