Archivio Istituzionale della RicercaA sharp Lp spectral multiplier theorem of Mihlin–Hörmander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation.
Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres / Ahrens, J.; Cowling, M. G.; Martini, A.; Muller, D.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 294:3-4(2020), pp. 1659-1686. [10.1007/s00209-019-02313-w]
Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
Martini A.;
2020
Abstract
A sharp Lp spectral multiplier theorem of Mihlin–Hörmander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation.
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quaternionic.pdf
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https://hdl.handle.net/11583/2949504