Spectral multipliers and wave equation for sub-Laplacians : lower regularity bounds of Euclidean type
Martini, A., Müller, D., & Nicolussi Golo, S. (2023). Spectral multipliers and wave equation for sub-Laplacians : lower regularity bounds of Euclidean type. Journal of the European Mathematical Society, 25(3), 785-843. https://doi.org/10.4171/JEMS/1191
Julkaistu sarjassa
Journal of the European Mathematical SocietyPäivämäärä
2023Tekijänoikeudet
© 2022 European Mathematical Society
Let 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 L cannot be wider than the corresponding ranges for the Laplace operator on Rn. 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 L and nondegeneracy properties of the sub-Riemannian geodesic flow.
Julkaisija
European Mathematical Society - EMS - Publishing House GmbHISSN Hae Julkaisufoorumista
1435-9855Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/103914213
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This research was partially supported by the EPSRC Grant “Sub-Elliptic Harmonic Analysis”(EP/P002447/1). Part of the work was carried out during a two-month visit of the first-named author to the Christian-Albrechts-Universität zu Kiel (Germany), made possible by the generous financial support of the Alexander von Humboldt FoundationLisenssi
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