Theresa C. Anderson, Laura Cladek, Malabika Pramanik, Andreas Seeger
Published 2018-01-22Version 1
Consider the surface measure $\mu$ on a sphere in a nonvertical hyperplane on the Heisenberg group $\mathbb{H}^n$, $n\ge 2$, and the convolution $f*\mu$. Form the associated maximal function $Mf=\sup_{t>0}|f*\mu_t|$ 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.
Analogues of theorems of Chernoff and Ingham on the Heisenberg group
An analogue of Ingham's theorem on the Heisenberg group
$L^p$ regularity for a class of averaging operators on the Heisenberg group
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