Mathematical Research Letters
Volume 13, Issue 6, November 2006 pp. 967-974.
Sharp $L^2\rightarrow L^q$ bounds on spectral projectors for low regularity metricsAuthors: Hart F. Smith
Author institution: University of Washington
Summary: We establish $L^2\rightarrow L^q$ mapping bounds for unit-width spectral projectors associated to elliptic operators with $C^s$ coefficients, in the case $1\le s\le 2$. Examples of Smith-Sogge \cite{SmSo} show that these bounds are best possible for $q$ less than the critical index. We also show that $L^\infty$ bounds hold with the same exponent as in the case of smooth coefficients.
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