Uniform pointwise estimates for ultraspherical polynomials

Valentina Casarino; Paolo Ciatti; Alessio Martini

doi:10.5802/crmath.255

Uniform pointwise estimates for ultraspherical polynomials

Valentina Casarino, Paolo Ciatti, Alessio Martini

Mathematics

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

Original language	English
Pages (from-to)	1239-1250
Number of pages	12
Journal	Comptes Rendus Mathematique
Volume	359
Issue number	10
DOIs	https://doi.org/10.5802/crmath.255
Publication status	Published - 4 Jan 2022

ASJC Scopus subject areas

General Mathematics

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title = "Uniform pointwise estimates for ultraspherical polynomials",

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

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AU - Casarino, Valentina

AU - Ciatti, Paolo

AU - Martini, Alessio

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N2 - 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.

AB - 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.

UR - https://arxiv.org/abs/2009.02323

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DO - 10.5802/crmath.255

M3 - Article

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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Uniform pointwise estimates for ultraspherical polynomials

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