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Abstract
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.
Original language | English |
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Pages (from-to) | 816-859 |
Journal | Advances in Mathematics |
Volume | 350 |
Early online date | 9 May 2019 |
DOIs | |
Publication status | Published - 9 Jun 2019 |
Keywords
- Grushin sphere
- associated Legendre functions
- spectral multipliers
- spherical harmonics
- sub-Laplacian
- sub-Riemannian geometry
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Dive into the research topics of 'From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere'. Together they form a unique fingerprint.Projects
- 1 Finished
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Sub-Elliptic Harmonic Analysis
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils