On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment
We study the following modification of the Landau–Kolmogorov problem: Let k; r ∈ ℕ, 1 ≤ k ≤ r − 1, and p, q, s ∈ [1,∞]. Also let MM^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 ever...
Збережено в:
Дата: | 2012 |
---|---|
Автор: | |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2012
|
Назва видання: | Український математичний журнал |
Теми: | |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164172 |
Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Цитувати: | On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment / D.S. Skorokhodov // Український математичний журнал. — 2012. — Т. 64, № 4. — С. 508-524. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraineid |
irk-123456789-164172 |
---|---|
record_format |
dspace |
spelling |
irk-123456789-1641722020-02-23T19:24:02Z On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment Skorokhodov, D.S. Статті We study the following modification of the Landau–Kolmogorov problem: Let k; r ∈ ℕ, 1 ≤ k ≤ r − 1, and p, q, s ∈ [1,∞]. Also let MM^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 We determine the quantity 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 MM^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 У данiй роботi величину знайдено у випадку s=∞ таm∈{r,r—1,r—2}. Також розглянуто деякi узагальнення вказаної модифiкацiї задачi Ландау – Колмогорова. 2012 Article On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment / D.S. Skorokhodov // Український математичний журнал. — 2012. — Т. 64, № 4. — С. 508-524. — Бібліогр.: 31 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/164172 517.5 en Український математичний журнал Інститут математики НАН України |
institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
collection |
DSpace DC |
language |
English |
topic |
Статті Статті |
spellingShingle |
Статті Статті Skorokhodov, D.S. On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment Український математичний журнал |
description |
We study the following modification of the Landau–Kolmogorov problem: Let k; r ∈ ℕ, 1 ≤ k ≤ r − 1, and p, q, s ∈ [1,∞]. Also let MM^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
We determine the quantity 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. |
format |
Article |
author |
Skorokhodov, D.S. |
author_facet |
Skorokhodov, D.S. |
author_sort |
Skorokhodov, D.S. |
title |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
title_short |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
title_full |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
title_fullStr |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
title_full_unstemmed |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
title_sort |
on inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment |
publisher |
Інститут математики НАН України |
publishDate |
2012 |
topic_facet |
Статті |
url |
http://dspace.nbuv.gov.ua/handle/123456789/164172 |
citation_txt |
On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment / D.S. Skorokhodov // Український математичний журнал. — 2012. — Т. 64, № 4. — С. 508-524. — Бібліогр.: 31 назв. — англ. |
series |
Український математичний журнал |
work_keys_str_mv |
AT skorokhodovds oninequalitiesforthenormsofintermediatederivativesofmultiplymonotonefunctionsdefinedonafinitesegment |
first_indexed |
2023-10-18T22:13:07Z |
last_indexed |
2023-10-18T22:13:07Z |
_version_ |
1796154943036456960 |