Herbert Koch, Hart F. Smith and Daniel Tataru Sharp $L^p$ bounds on spectral clusters for Lipschitz metrics Amer. J. Math., 136(6): 1629-1663 2014 http://dx.doi.org/10.1353/ajm.2014.0039
Abstract: We establish Lp bounds on L2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all 2 ≤ p ≤ ∞, up to logarithmic losses for 6 < p ≤ 8. In higher dimensions we obtain best possible bounds for a limited range of p.