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Sharp Lp Bounds on Spectral Clusters for Lipschitz Metrics
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 6, December 2014
- pp. 1629-1663
- 10.1353/ajm.2014.0039
- Article
- Additional Information
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We establish $L^p$ bounds on $L^2$ normalized spectral clusters for self-adjoint elliptic Dirichlet forms
with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all $2\le p\le\infty$,
up to logarithmic losses for $6<p\le 8$. In higher dimensions we obtain best possible bounds for a limited
range of $p$.