Bernstein-Szeg\H o inequality for the Riesz derivative of~trigonometric polynomials in $L_p$-spaces, $0\leqslant p\leqslant\infty$, with classical value of the sharp constant
Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 411-428
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The Bernstein-Szegő inequality for the Weyl derivative of real order $\alpha\geqslant 0$ 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 $n^\alpha$ (the classical value) in all $L_p$-spaces, $0\leqslant p\leqslant\infty$. The set of all such $\alpha$ 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 $n\in\mathbb N$.
Bibliography: 22 titles.
Keywords:
trigonometric polynomial, Riesz derivative, Bernstein-Szegő inequality, space $L_0$.
@article{SM_2023_214_3_a6,
author = {A. O. Leont'eva},
title = {Bernstein-Szeg\H o inequality for the {Riesz} derivative of~trigonometric polynomials in $L_p$-spaces, $0\leqslant p\leqslant\infty$, with classical value of the sharp constant},
journal = {Sbornik. Mathematics},
pages = {411--428},
publisher = {mathdoc},
volume = {214},
number = {3},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2023_214_3_a6/}
}
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A. O. Leont'eva. Bernstein-Szeg\H o inequality for the Riesz derivative of~trigonometric polynomials in $L_p$-spaces, $0\leqslant p\leqslant\infty$, with classical value of the sharp constant. Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 411-428. http://geodesic.mathdoc.fr/item/SM_2023_214_3_a6/