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arXiv · 1801.06981

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

Theresa C. Anderson·Laura Cladek·Malabika Pramanik·Andreas Seeger
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Abstract

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.

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Theresa C. Anderson, Laura Cladek, Malabika Pramanik, Andreas Seeger. 2018-01-22. Spherical means on the Heisenberg group: Stability of a maximal function estimate. https://arxiv.org/abs/1801.06981

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