Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers-Reference-Cited by-同舟云学术

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Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers

Published:2023 Issue:1 Volume:214 Page:1-27
ISSN:1064-5616
Container-title:Sbornik: Mathematics
language:en
Short-container-title:Sb. Math.

Author:

Vinogradov Oleg Leonidovich¹

Affiliation:

1. Saint Petersburg State University, St. Petersburg, Russia

Abstract

A method for the proof of analogues of the classical Bernstein, Riesz and Boas inequalities for differentiation and difference operators defined by means of multipliers in terms of the Fourier-Dunkl transform is developed. This method is based on Civin-type interpolation formulae. Some of the inequalities obtained are sharp in the uniform norm. Bibliography: 42 titles.

Funder

Russian Science Foundation

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

Reference55 articles.

1. Math. Lehrbücher und Monogr.;N. I. Achieser,1967

2. Internat. Ser. Monogr. Pure Appl. Math.;A. F. Timan,1963

3. Sur l'ordre de la meilleure approximation des fonctions continues par des polynomes de degré donné;S. N. Bernstein;Mem. Acad. Roy. Belgique, 2e série,1912

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