English

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

R2 v1 2026-06-23T18:19:29.775Z