On Kolmogorov-type inequalities with integrable highest derivative

被引：0
|
作者：
Babenko V.F. [1 ]
Kofanov V.A. [1 ]
Pichugov S.A. [1 ]
机构：
[1] Dnepropetrovsk University, Dnepropetrovsk
来源：
Ukrainian Mathematical Journal | 2002年 / 54卷 / 12期
关键词：
High Derivative; Integrable High;
D O I：
10.1023/A:1024085601336
中图分类号：
学科分类号：
摘要：
We obtain the new exact Kolmogorov-type inequality ∥x (k)∥2 ≤ K∥x∥2 r-k-1/2/r-1/2∥x(r)∥1k/r-1/2 for 2π-periodic functions x ∈ L1r and any k, r ∈ N, k < r. We present applications of this inequality to problems of approximation of one class of functions by another class and estimates of K-functional type. © 2002 Plenum Publishing Corporation.
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页码：2055 / 2059
页数：4
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