Spectral multipliers for the Kohn sublaplacian on the sphere in $\mathbb {C}^n$
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- by Michael G. Cowling, Oldrich Klima and Adam Sikora PDF
- Trans. Amer. Math. Soc. 363 (2011), 611-631 Request permission
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 $S$.References
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Additional Information
- Michael G. Cowling
- Affiliation: School of Mathematics, University of New South Wales, UNSW Sydney 2052, Australia
- MR Author ID: 52360
- ORCID: 0000-0003-0995-3054
- 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
- MR Author ID: 292432
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 611-631
- MSC (2010): Primary 42B15; Secondary 43A85, 32V20
- DOI: https://doi.org/10.1090/S0002-9947-2010-04920-7
- MathSciNet review: 2728580