Uniform pointwise estimates for ultraspherical polynomials

Casarino, Valentina; Ciatti, Paolo; Martini, Alessio

Comptes Rendus. Mathématique, Tome 359 (2021) no. 10, pp. 1239-1250.

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, discussed in a companion paper, of sharp multiplier theorems for those operators.

Classification : 33C45, 33C55, 42C05, 58J50

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