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An (n + 1)– fold Marcinkiewicz multiplier theorem on the Heisenberg group

Published online by Cambridge University Press:  17 April 2009

A. J. Fraser
A. J. Fraser
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
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Abstract

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We prove a Marcinkiewicz-type multiplier theorem on the Heisenberg group: for 1 < p < ∞, we establish the boundedness on Lp (ℍn) of spectral multipliers m (ℒ1,…,ℒn, iT) of the n partial sub-Laplacians ℒ1,…,ℒn and iT, where m satisfies an (n + l)-fold Marcinkiewicz-type condition. We also establish regularity and cancellation conditions which the convolution kernels of these Marcinkiewicz multipliers m (ℒ1,…,ℒn,iT) satisfy.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 35 - 58
Copyright
Copyright © Australian Mathematical Society 2001

References

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