Kakeya maximal inequality in the Heisenberg group

Katrin Fässler, Andrea Pinamonti, Pietro Wald

We define the Heisenberg Kakeya maximal functions $M_{\delta }f$, $0<\delta <1$, by averaging over $\delta$-neighborhoods of horizontal unit line segments in the Heisenberg group ${\mathbb{H}}^1$ equip…