Mathematical Research Letters

Volume 14, Issue 1, January 2007 pp. 77-85.

Sharp $L^q$ bounds on spectral clusters for Holder metrics

Authors: Herbert Koch (1), Hart F. Smith (2), and Daniel Tataru (3)
Author institution: Universität Bonn (1), University of Washington (2), and University of California, Berkeley (3)

Summary: We establish $L^q$ 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 $C^s$, where $0\le s\le 1$. We also produce examples which show that these bounds are best possible for the case $q=\infty$, and for $2\le q\le q_n$.

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