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

Valentina Casarino, Paolo Ciatti, Alessio Martini

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
122 Downloads (Pure)

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 languageEnglish
Pages (from-to)816-859
JournalAdvances in Mathematics
Volume350
Early online date9 May 2019
DOIs
Publication statusPublished - 9 Jun 2019

Keywords

  • Grushin sphere
  • associated Legendre functions
  • spectral multipliers
  • spherical harmonics
  • sub-Laplacian
  • sub-Riemannian geometry

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