Sharp $L^p$-bounds for the wave equation on groups of Heisenberg type

TL;DR

This paper establishes sharp $L^p$ bounds for the wave equation on groups of Heisenberg type by constructing parametrices with oscillatory integrals, leading to optimal regularity results in $L^p$ and Hardy spaces.

Contribution

It introduces a novel parametrix construction for the wave equation on Heisenberg-type groups, achieving sharp regularity bounds in $L^p$ and Hardy spaces.

Findings

Proved sharp $L^p$ bounds for the wave equation

Established optimal Hardy space regularity results

Developed oscillatory integral parametrices for the Kohn Laplacian

Abstract

Consider the wave equation associated with the Kohn Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp $L^p$ and Hardy space regularity results.