Spectral cluster estimates for C1,1 metrics

In this paper, we establish L^p norm bounds for spectral clusters on compact manifolds, under the assumption that the metric is C^1,1. Precisely, we show that the L^p estimates proven by Sogge in the case of smooth metrics hold under this limited regularity assumption. It is known by examples of Smith-Sogge that such estimates fail for C^1,α metrics if α < 1.