Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems
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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.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3583-3599
- MSC (2010): Primary 35P20, 35J25, 58J05, 58J32, 58J40, 35P15, 35J05
- DOI: https://doi.org/10.1090/S0002-9939-2011-10782-2
- MathSciNet review: 2813389