Comptes Rendus
Harmonic analysis
Uniform pointwise estimates for ultraspherical polynomials
Comptes Rendus. Mathématique, Volume 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.

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DOI: 10.5802/crmath.255
Classification: 33C45, 33C55, 42C05, 58J50

Valentina Casarino 1; Paolo Ciatti 2; Alessio Martini 3

1 Università degli Studi di Padova, DTG, Stradella san Nicola 3, I-36100 Vicenza, Italy
2 Università degli Studi di Padova, DICEA, Via Marzolo 9, I-35100 Padova, Italy
3 School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Valentina Casarino; Paolo Ciatti; Alessio Martini. Uniform pointwise estimates for ultraspherical polynomials. Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1239-1250. doi : 10.5802/crmath.255. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.255/

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