Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems

Xu, Xiangjin

doi:10.1090/S0002-9939-2011-10782-2

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
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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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