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
DOI:
https://doi.org/10.1090/S0002-9939-2011-10782-2
Published electronically:
March 3, 2011
MathSciNet review:
2813389
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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.