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

• Autores: Herbert Koch , Hart F. Smith, Daniel Tataru
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 1, 2007, págs. 77-85
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n1.a6
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• Resumen

  • 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 $2\le q\le q_n$.