Bernstein-Szegő inequality for the Riesz derivative of trigonometric polynomials in Lp-spaces, 0 ⩽ p ⩽ ∞, with classical value of the sharp constant

Abstract

The Bernstein-Szegő inequality for the Weyl derivative of real order α ⩾ 0 of trigonometric polynomials of degree n is considered. The aim is to find values of the parameters for which the sharp constant in this inequality is equal to nα (the classical value) in all Lp-spaces, 0 ⩽ p ⩽ ∞. The set of all such α is described for some important particular cases of the Weyl-Szegő derivative, namely, for the Riesz derivative and for the conjugate Riesz derivative, for all n ∈ N. © 2023 Russian Academy of Sciences,.