Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers

O. L. Vinogradov

Sbornik. Mathematics, Tome 214 (2023) no. 1, pp. 1-27

Résumé

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.

Détail

Keywords: Bernstein, Riesz, and Boas inequalities, Dunkl operator
Mots-clés : sharp constant.

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