Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space L0

被引：5

作者：

Leont'eva, A. O. ^{[1
,2
]}

机构：

[1] Yeltsin Ural Fed Univ, Ekaterinburg 620002, Russia

[2] Russian Acad Sci, Ural Branch, Krasovskii Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

MATHEMATICAL NOTES | 2018年 / 104卷 / 1-2期

关键词：

trigonometric polynomial; Weyl derivative; Bernstein's inequality; the space L-0;

D O I：

10.1134/S0001434618070271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：263 / 270

页数：8

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