Detlef Müller, Elias M. Stein
Abstract
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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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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| .
Key concepts: Heisenberg group, Physics, Mathematical physics, Group (periodic table), Mathematics, Mathematical analysis, Quantum mechanics