Kolmogorov-type inequalities for mixed derivatives of functions of many variables

被引：0
|
作者：
Babenko V.F. [1 ,2 ]
Korneichuk N.P.
Pichugov S.A. [1 ,3 ]
机构：
[1] Dnepropetrovsk University, Dnepropetrovsk
[2] Institute for Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk
[3] Dnepropetrovsk Agricultural University, Dnepropetrovsk
来源：
Ukrainian Mathematical Journal | 2004年 / 56卷 / 5期
关键词：
Positive Component; Mixed Derivative;
D O I：
10.1007/s11253-005-0066-1
中图分类号：
学科分类号：
摘要：
Let γ = (γ1,...,γd) be a vector with positive components and let D γ be the corresponding mixed derivative (of order γ j with respect to the j th variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that sup equation presented at =∞ and equation presented at for all x ∈ L ∞rγ (T d). Moreover, if β̄ is the least possible value of the exponent β in this inequality, then (d-1)(1-k/r)≤ β̄(d, γ,k,r) ≤ d - 1. © 2004 Springer Science+Business Media, Inc.
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页码：699 / 717
页数：18
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