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- W2916506860 endingPage "843" @default.
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- W2916506860 abstract "Let $mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mikhlin–Hörmander type and wave propagator estimates of Miyachi–Peral type for $mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $mathbb{R}^n$. The result applies to all sub-Laplacians on Carnot groups and more general sub-Riemannian manifolds, without restrictions on the step. The proof hinges on a Fourier integral representation for the wave propagator associated with $mathscr{L}$ and nondegeneracy properties of the sub-Riemannian geodesic flow." @default.
- W2916506860 created "2019-03-02" @default.
- W2916506860 creator A5028748648 @default.
- W2916506860 creator A5036963156 @default.
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- W2916506860 date "2022-01-04" @default.
- W2916506860 modified "2023-09-24" @default.
- W2916506860 title "Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type" @default.
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- W2916506860 doi "https://doi.org/10.4171/jems/1191" @default.
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