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Mathematical Research Letters
Volume 14 (2007)
Number 1
Sharp $L^q$ bounds on spectral clusters for Holder metrics
Pages: 77 – 85
DOI: https://dx.doi.org/10.4310/MRL.2007.v14.n1.a6
Authors
Abstract
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 $2\le q\le q_n$.
Published 1 January 2007