A new proof of maximal theorem on Heisenberg groups

Chuhan Sun, Zipeng Wang

Given $0\le \alpha <1$, we define \[\begin{array}{lr} \mathbf{M}_αf(u,v,t) = \sup_{ \mathbf{R} \ni (0,0,0)} {\rm vol} \{\mathbf{R}\}^{α-1} \iiint_\mathbf{R}\left|f [(u,v,t)\odot(ξ,η,τ)^{…