Uniform pointwise estimates for ultraspherical polynomials
Classical Analysis and ODEs
2022-02-28 v1
Abstract
We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof of sharp multiplier theorems for those operators.
Keywords
Cite
@article{arxiv.2009.02323,
title = {Uniform pointwise estimates for ultraspherical polynomials},
author = {Valentina Casarino and Paolo Ciatti and Alessio Martini},
journal= {arXiv preprint arXiv:2009.02323},
year = {2022}
}
Comments
12 pages. This work extends the estimates for spherical harmonics initially proved in arXiv:1705.07068