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arXiv · 1705.07068

From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

Valentina Casarino·Paolo Ciatti·Alessio Martini
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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 $\mathbb{R}^3$, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.

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Valentina Casarino, Paolo Ciatti, Alessio Martini. 2017-05-19. From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere. https://doi.org/10.1016/j.aim.2019.05.003

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