Vol. 95, No. 1, 1981

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Zonal multipliers on the Heisenberg group

Giancarlo Mauceri

Vol. 95 (1981), No. 1, 143–159
Abstract

We investigate Lp 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 Lp 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
Authors
Giancarlo Mauceri