JournalsrmiVol. 15, No. 2pp. 297–334

LpL^p-estimates for the wave equation on the Heisenberg group

  • Detlef Müller

    Christian-Albrechts-Universität zu Kiel, Germany
  • Elias M. Stein

    Princeton University, United States
$L^p$-estimates for the wave equation on the Heisenberg group cover
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Abstract

Let L\mathcal L denote the sub-Laplacian on the Heisenberg group Hm\mathbb H_m. We prove that eiLe^{i\sqrt {–\mathcal L}} /(1L)α/2/(1 – \mathcal L)^{\alpha/2} extends to a bounded operator on Lp(Hm)L^p (\mathbb H_m), for 1p1 ≤ p ≤ \infty, when α>(d1)1/p1/2\alpha > (d–1) | 1/p – 1/2|.

Cite this article

Detlef Müller, Elias M. Stein, LpL^p-estimates for the wave equation on the Heisenberg group. Rev. Mat. Iberoam. 15 (1999), no. 2, pp. 297–334

DOI 10.4171/RMI/258