Heisenberg Hausdorff Dimensionof Besicovitch Sets

Abstract

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

Keywords

• besicovitch set
• kakeya maximal function
• heisenberg group
• hausdorff dimension