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We prove a sharp multiplier theorem of Mihlin–H¨ormander type for the Grushin operator on the unit sphere in R3, and a corresponding boundedness result for the associated Bochner–Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.
|Journal||Advances in Mathematics|
|Early online date||9 May 2019|
|Publication status||Published - 9 Jun 2019|
- Grushin sphere
- associated Legendre functions
- spectral multipliers
- spherical harmonics
- sub-Riemannian geometry
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- 1 Finished
Sub-Elliptic Harmonic Analysis
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils