Spherical means on the Heisenberg group: Stability of a maximal function estimate

Consider the surface measure $μ$ on a sphere in a nonvertical hyperplane on the Heisenberg group $\mathbb{H}^n$, $n\ge 2$, and the convolution $f*μ$. Form the associated maximal function $Mf=\sup_{t>0}|f*μ_t|$ generated by the automorphic dilations. We use decoupling inequalities due to Wolff and Bourgain-Demeter to prove $L^p$-boundedness of $M$ in an optimal range.

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