Zonal multipliers on the Heisenberg group

Giancarlo Mauceri

Vol. 95 (1981), No. 1, 143–159

DOI: 10.2140/pjm.1981.95.143

Abstract

We investigate L^p boundedness of zonal multipliers on the 2n + 1-dimensional Heisenberg group Hⁿ. These are multipliers which are invariant under the group SU(n) acting in the noncentral variables. The result is then applied to derive sufficient conditions for L^p boundedness for a class of multipliers associated with SU(n) invariant operators in the enveloping algebra of Hⁿ. A necessary condition is also obtained with the aid of group contractions.

Mathematical Subject Classification 2000

Primary: 43A80

Secondary: 22E30, 43A22, 58G05

Milestones

Received: 31 July 1979

Revised: 24 June 1980

Published: 1 July 1981