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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spectral multipliers for the Kohn sublaplacian on the sphere in $ \mathbb{C}^n$


Authors: Michael G. Cowling, Oldrich Klima and Adam Sikora
Journal: Trans. Amer. Math. Soc. 363 (2011), 611-631
MSC (2010): Primary 42B15; Secondary 43A85, 32V20
Published electronically: September 22, 2010
MathSciNet review: 2728580
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Abstract: The unit sphere $ S$ in $ \mathbb{C}^n$ has a natural sublaplacian $ \mathcal{L}$. We prove that the critical index for a Hörmander spectral multiplier theorem for  $ \mathcal{L}$ is $ n-1/2$, that is, half the topological dimension of $ S$.


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Additional Information

Michael G. Cowling
Affiliation: School of Mathematics, University of New South Wales, UNSW Sydney 2052, Australia

Oldrich Klima
Affiliation: School of Mathematics, University of New South Wales, UNSW Sydney 2052, Australia
Address at time of publication: DPMMS, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

Adam Sikora
Affiliation: Department of Mathematics, University of New Mexico, Albuquerque, New Mexico 87131
Address at time of publication: Department of Mathematics, E7A 418, Macquarie University, NSW Sydney 2109, Australia

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04920-7
PII: S 0002-9947(2010)04920-7
Received by editor(s): October 2, 2006
Received by editor(s) in revised form: July 27, 2008
Published electronically: September 22, 2010
Additional Notes: This work was supported by an Australian Postgraduate Research Award, the Australian Research Council, and the University of New South Wales. It is a pleasure to thank the anonymous referee for his or her careful reading and constructive criticism of this paper.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.