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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

New proof of the Hörmander multiplier theorem on compact manifolds without boundary


Author: Xiangjin Xu
Journal: Proc. Amer. Math. Soc. 135 (2007), 1585-1595
MSC (2000): Primary 58J40, 35P20, 35J25
Published electronically: January 9, 2007
MathSciNet review: 2276671
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Abstract: On compact manifolds $ (M, g)$ without boundary, the gradient estimates for unit band spectral projection operators $ \chi_{\lambda}$ are proved for a second order elliptic differential operator $ L$. A new proof of the Hörmander Multiplier Theorem (first proved by A. Seeger and C.D. Sogge in 1989) is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.


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Additional Information

Xiangjin Xu
Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720
Address at time of publication: Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, Virginia 22904
Email: xiangjxu@msri.org, xx8n@virginia.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08687-X
PII: S 0002-9939(07)08687-X
Keywords: Gradient estimate, eigenfunction, unit band spectral projection operator, H\"ormander Multiplier Theorem
Received by editor(s): September 15, 2005
Received by editor(s) in revised form: February 28, 2006
Published electronically: January 9, 2007
Communicated by: Andreas Seeger
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.