RADIAL MULTIPLIERS FOR THE HEISENBERG-GROUP

Let G be a locally compact abelian group and GAMMA its dual group; the following theorem is due to H. Helson [1]: let PHI be a multiplier of A (GAMMA) into B (GAMMA); then PHI is-an-element-of B (GAMMA). We extend this theorem to a setup including radial measures or functions on the Heisenberg group. Our methods use Banach algebras techniques and as far as the power type growth is concerned, the symbolic calculus of J. Dixmier [2] is essential.