Lp-estimates for the wave equation on the Heisenberg group

Abstract

Let ℒ denote the sub-Laplacian on the Heisenberg group ℍm. We prove that ei√-ℒ/(1 - ℒ)α/2 extends to a bounded operator on Lp(ℍm), for 1 ≤ p ≤ ∞ when α > (d - 1)\1/p - 1/2|.