Strict inequalities for the derivatives of functions satisfying certain boundary conditions

Zvyagintsev, A. I.

doi:10.1007/bf02361298

Cited by 1 publication

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References 5 publications

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“…Remark that in papers [22,14,6,30,29,26] it was shown that Problems 1 and 2 could be solved completely if they are considered not on the whole space L r s but on some its subset X. In this paper we concern with the study of Problems 1 and 2 as well as their generalizations on the classes of functions that are multiply monotone on the interval [0,1].…”

Section: Introduction and Statement Of The Problemmentioning

confidence: 99%

On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

Skorokhodov

2012

Ukr Math J

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Also let M M m , m ∈ N, be the class of nonnegative functions defined on the segment [0, 1] whose derivatives of orders 1, 2,. .. , m are nonnegative almost everywhere on [0, 1]. For every δ > 0, find the exact value of the quantity ω k,r p,q,s (δ; M M m) := sup x (k) q : x ∈ M M m , x p ≤ δ, x (r) s ≤ 1. We determine the quantity ω k,r p,q,s (δ; M M m) in the case where s = ∞ and m ∈ {r, r − 1, r − 2}. In addition, we consider certain generalizations of the above-stated modification of the Landau-Kolmogorov problem. Дослiджується наступна модифiкацiя задачi Ландау-Колмогорова. Нехай k, r ∈ N, 1 ≤ k ≤ r − 1, p, q, s ∈ [1, ∞] i M M m , m ∈ N,-клас невiд'ємних функцiй, що заданi на вiдрiзку [0, 1] та мають майже скрiзь на [0, 1] невiд'ємнi похiднi порядкiв 0, 1,. .. , m. Для кожного δ > 0 необхiдно знайти величину ω k,r p,q,s (δ; M M m) := sup x (k) q : x ∈ M M m , x p ≤ δ, x (r) s ≤ 1. У данiй роботi величину ω k,r p,q,s (δ; M M m) знайдено у випадку s = ∞ та m ∈ {r, r − 1, r − 2}. Також розглянуто деякi узагальнення вказаної модифiкацiї задачi Ландау-Колмогорова.

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Section: Introduction and Statement Of The Problemmentioning

confidence: 99%

On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

Skorokhodov

2012

Ukr Math J

View full text Add to dashboard Cite

show abstract

Strict inequalities for the derivatives of functions satisfying certain boundary conditions

Cited by 1 publication

References 5 publications

On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

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