Hörmander Multipliers on the Heisenberg Group

Abstract.

 Let be the Heisenberg group of dimension . Let be the partial sub-Laplacians on and T the central element of the Lie algebra of . For any we prove that the operator is bounded on the Hardy spaces , if the function m satisfies a Hrmander-type condition on which depends on . We also obtain analogous results for the operators and , where the function m satisfies analogous Hörmander-type conditions on and on , respectively. Here is the Kohn-Laplacian on .