Abstract
We study degenerate elliptic operators of Grushin type on the d-dimensional sphere, which are singular on a k-dimensional sphere for some k<d. For these operators we prove a spectral multiplier theorem of Mihlin–Hörmander type, which is optimal whenever 2k≤d, and a corresponding Bochner–Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.
Original language | English |
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Article number | rnab007 |
Journal | International Mathematics Research Notices |
Early online date | 10 Mar 2021 |
DOIs | |
Publication status | E-pub ahead of print - 10 Mar 2021 |