Revista Matemática Iberoamericana


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Volume 15, Issue 2, 1999, pp. 297–334
DOI: 10.4171/RMI/258

Published online: 1999-08-31

$L^p$-estimates for the wave equation on the Heisenberg group

Detlef Müller[1] and Elias M. Stein[2]

(1) Christian-Albrechts-Universität zu Kiel, Germany
(2) Princeton University, United States

Let $\mathcal L$ denote the sub-Laplacian on the Heisenberg group $\mathbb H_m$. We prove that $e^{i\sqrt {–\mathcal L}}$ $/(1 – \mathcal L)^{\alpha/2}$ extends to a bounded operator on $L^p (\mathbb H_m)$, for $1 ≤ p ≤ \infty$, when $\alpha > (d–1) | 1/p – 1/2|$.

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Müller Detlef, Stein Elias: $L^p$-estimates for the wave equation on the Heisenberg group. Rev. Mat. Iberoam. 15 (1999), 297-334. doi: 10.4171/RMI/258