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

 

Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems


Author: Xiangjin Xu
Journal: Proc. Amer. Math. Soc. 139 (2011), 3583-3599
MSC (2010): Primary 35P20, 35J25, 58J05, 58J32, 58J40, 35P15, 35J05
Published electronically: March 3, 2011
MathSciNet review: 2813389
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Abstract: On compact Riemannian manifolds with boundary, the $ L^{\infty}$ estimates and gradient estimates for the eigenfunctions of the Neumann Laplacian are proved. Applying the $ L^p$ estimates and gradient estimates to multiplier problems on eigenfunction expansions for the Neumann Laplacian, some new estimates for Bochner Riesz means and the sharp Hörmander Multiplier Theorem are obtained.


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Additional Information

Xiangjin Xu
Affiliation: Department of Mathematical Sciences, Binghamton University, State University of New York, Binghamton, New York 13902
Email: xxu@math.binghamton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10782-2
PII: S 0002-9939(2011)10782-2
Keywords: $L^{\infty}$ estimate, gradient estimate, spectral cluster, Neumann Laplacian, Bochner Riesz means, Hörmander Multiplier Theorem
Received by editor(s): May 11, 2010
Received by editor(s) in revised form: August 26, 1010
Published electronically: March 3, 2011
Additional Notes: The author’s research was supported by the National Science Foundation under grants DMS-0602151 and DMS-0852507.
Communicated by: Hart F. Smith
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.