L Bounds for Spectral Clusters
نویسنده
چکیده
In these notes, we review recent results concerning the Lp norm bounds for spectral clusters on compact manifolds. The type of estimates we consider were first established by Sogge [15] in the case of smooth metrics. Recent results of ours in [10] establish the same estimates under the assumption that the metric is C1,1. It is known by examples of Smith-Sogge [12] that such estimates fail for C1,α metrics if α < 1, and we discuss methods for obtaining slightly weaker results in this setting also.
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