On the$L$^{$p$}norm of spectral clusters for compact manifolds with boundary

Hart F. Smith Department of Mathematics, University of Washington Christopher D. Sogge Department of Mathematics, Johns Hopkins University

TBD mathscidoc:1701.331981

Acta Mathematica, 198, (1), 107-153, 2005.11
We use microlocal and paradifferential techniques to obtain$L$^{8}norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal$L$^{$q$}bounds, in the range 2⩽q⩽∞, for$L$^{2}- normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp$L$^{$q$}estimates in higher dimensions for a range of exponents q̅_{n}⩽$q$⩽∞.
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@inproceedings{hart2005on,
  title={On the$L$^{$p$}norm of spectral clusters for compact manifolds with boundary},
  author={Hart F. Smith, and Christopher D. Sogge},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203350347205690},
  booktitle={Acta Mathematica},
  volume={198},
  number={1},
  pages={107-153},
  year={2005},
}
Hart F. Smith, and Christopher D. Sogge. On the$L$^{$p$}norm of spectral clusters for compact manifolds with boundary. 2005. Vol. 198. In Acta Mathematica. pp.107-153. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203350347205690.
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