Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

Abstract

A sharp $L^p$ 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.

References in corpus (1)

• Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

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