Sharp L Bounds on Spectral Clusters for Holder Metrics
نویسندگان
چکیده
We establish Lq bounds on eigenfunctions, and more generally on spectrally localized functions (spectral clusters), associated to a self-adjoint elliptic operator on a compact manifold, under the assumption that the coefficients of the operator are of regularity Cs, where 0 ≤ s ≤ 1. We also produce examples which show that these bounds are best possible for the case q =∞, and for 2 ≤ q ≤ qn.
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تاریخ انتشار 2006