Hörmander multipliers on the Heisenberg group (Q1585700)

Let \(\mathbb{H}_n\) be the Heisenberg group of dimension \(2n+1\). Let \({\mathcal L}_1, \dots, {\mathcal L}_n\) be the partial sub-Laplacians on \(\mathbb{H}_n\) and \(T\) the central element of the Lie algebra of \(\mathbb{H}_n\). For \(0<p_0\leq 1\), the author proves that the operator \(m({\mathcal L}_1, \dots, {\mathcal L}_n, -iT)\) is bounded on the Hardy spaces \(H^p(\mathbb{H}_n)\), \(p_0\leq p<\infty\), if the function \(m\) satisfies a Hörmander type condition on \(\mathbb{R}^{n+1}\) which depends on \(p_0\). Let \({\mathcal L}={\mathcal L}_1 +\cdots+ {\mathcal L}_n\) be the Kohn Laplacian on \(\mathbb{H}_n\). The author also obtains analogous results for the operators \(m({\mathcal L}, -iT)\) and \(m({\mathcal L}_1, \dots, {\mathcal L}_n)\), where the function \(m\) satisfies analogous Hörmander type conditions.