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arXiv · 2002.01917

$L^p$ regularity for a class of averaging operators on the Heisenberg group

Geoffrey Bentsen
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Abstract

We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all $L^p$ functions boundedly.

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Geoffrey Bentsen. 2020-02-05. $L^p$ regularity for a class of averaging operators on the Heisenberg group. https://arxiv.org/abs/2002.01917

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