Sharp L^p bounds on spectral clusters for Lipschitz metrics

Herbert Koch; Hart Smith; Daniel Tataru

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arXiv · 1207.2417

Sharp L^p bounds on spectral clusters for Lipschitz metrics

Herbert Koch·Hart Smith·Daniel Tataru

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Abstract

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 p between $2 and infinity, up to logarithmic losses for $6<p\leq 8$. In higher dimensions we obtain best possible bounds for a limited range of p.

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Herbert Koch, Hart Smith, Daniel Tataru. 2012-07-10. Sharp L^p bounds on spectral clusters for Lipschitz metrics. https://arxiv.org/abs/1207.2417

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