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
DOI:
https://doi.org/10.1090/S0002-9939-07-08687-X
Published electronically:
January 9, 2007
MathSciNet review:
2276671
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Keywords:
Gradient estimate,
eigenfunction,
unit band spectral projection operator,
Hörmander 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.
