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Convolution kernels of (n + 1)-fold Marcinkiewicz multipliers on the Heisenberg group

Published online by Cambridge University Press:  17 April 2009

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

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We prove a characterisation, in terms of regularity and cancellation conditions, of the convolution kernels of Marcinkiewicz multiplier operators m (𝔏1,…,𝔏n, iT) on the Heisenberg group ℍn, where 𝔏1,…,𝔏n are the n partial sub-Laplacians. The necessity of these regularity and cancellation conditions was established by Fraser (2001); here, we prove their sufficiency.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 353 - 376
Copyright
Copyright © Australian Mathematical Society 2001

References

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