We prove a sharp multiplier theorem of Mihlin--H"ormander type for the Grushin operator on the unit sphere in $RR^3$, and a corresponding boundedness result for the associated Bochner--Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.
From refined estimates for the spherical harmonics to a sharp multiplier theorem on the Grushin sphere
CASARINO, VALENTINA;CIATTI, PAOLO;MARTINI, ALESSIO
2019
Abstract
We prove a sharp multiplier theorem of Mihlin--H"ormander type for the Grushin operator on the unit sphere in $RR^3$, and a corresponding boundedness result for the associated Bochner--Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.File in questo prodotto:
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