New proof of the Hörmander multiplier theorem on compact manifolds without boundary
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- by Xiangjin Xu
- Proc. Amer. Math. Soc. 135 (2007), 1585-1595
- DOI: https://doi.org/10.1090/S0002-9939-07-08687-X
- Published electronically: January 9, 2007
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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.References
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Bibliographic 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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1585-1595
- MSC (2000): Primary 58J40, 35P20, 35J25
- DOI: https://doi.org/10.1090/S0002-9939-07-08687-X
- MathSciNet review: 2276671