Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators
Research output: Contribution to journal › Article › peer-review
Colleges, School and Institutes
- Universita di Padova
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.
|Journal||International Mathematics Research Notices|
|Early online date||10 Mar 2021|
|Publication status||E-pub ahead of print - 10 Mar 2021|