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Marcinkiewicz multipliers on the Heisenberg group

Published online by Cambridge University Press:  17 April 2009

Alessandro Veneruso
Alessandro Veneruso
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy, e-mail: veneruso@dima.unige.it
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Abstract

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Let Hn be the Heisenberg group of dimension 2n + 1. Let ℒ1,…,ℒn be the partial sub-Laplacians on Hn and T the central element of the Lie algebra of Hn. We prove that the operator m (ℒ1,…,ℒn,−iT) is bounded on Lp (Hn), 1 < p < +∞, if the function m satisfies a Marcinkiewicz-type condition in Rn+1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 53 - 68
Copyright
Copyright © Australian Mathematical Society 2000

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