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Mat. Zametki, 2018, Volume 104, Issue 2, Pages 255–264 (Mi mz11757)  

This article is cited in 2 scientific papers (total in 2 papers)

Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space $L_0$

A. O. Leont'evaab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: A logarithmic asymptotics for the behavior with respect to $n$ of the exact constant in Bernstein's inequality for the Weyl derivative of positive noninteger order of trigonometric polynomials of order $n$ in the space $L_0$ is obtained. It turns out that the order in $n$ of the behavior of this constant for positive noninteger orders of the derivatives has exponential growth in contrast to the power growth in the well-studied case of classical derivatives of positive integer order.

Keywords: trigonometric polynomial, Weyl derivative, Bernstein's inequality, the space $L_0$.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-9356.2016.1
02.A03.21.0006


DOI: https://doi.org/10.4213/mzm11757

Full text: PDF file (514 kB)
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English version:
Mathematical Notes, 2018, 104:2, 263–270

Bibliographic databases:

UDC: 517
Received: 26.07.2017
Revised: 07.10.2017

Citation: A. O. Leont'eva, “Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space $L_0$”, Mat. Zametki, 104:2 (2018), 255–264; Math. Notes, 104:2 (2018), 263–270

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. O. Leonteva, “Neravenstvo Bernshteina - Sege dlya proizvodnoi Veilya trigonometricheskikh polinomov v prostranstve $L_0$”, Tr. IMM UrO RAN, 24, no. 4, 2018, 199–207  mathnet  crossref  elib
    2. A. O. Leonteva, “Neravenstvo Bernshteina - Sege v prostranstve $L_0$ dlya trigonometricheskikh polinomov”, Tr. IMM UrO RAN, 25, no. 4, 2019, 129–135  mathnet  crossref  elib
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