Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment
For arbitrary t ∈ [0, 1], s ∈ [1, ∞], and A ≥ 2, we determine the unimprovable constant B for the inequality $$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$ .
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4239 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510369253949440 |
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| author | Babenko, Yu. V. Бабенко, Ю. В. Бабенко, Ю. В. |
| author_facet | Babenko, Yu. V. Бабенко, Ю. В. Бабенко, Ю. В. |
| author_sort | Babenko, Yu. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:08Z |
| description | For arbitrary t ∈ [0, 1], s ∈ [1, ∞], and A ≥ 2, we determine the unimprovable constant B for the inequality $$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$ . |
| first_indexed | 2026-03-24T02:55:54Z |
| format | Article |
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| id | umjimathkievua-article-4239 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:55:54Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/fb/e9cd5ea73129ce5edc9f41f9a253a2fb.pdf |
| spelling | umjimathkievua-article-42392020-03-18T20:25:08Z Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment Поточечные неравенства типа Ландау - Колмогорова для функций, заданных на конечном отрезке Babenko, Yu. V. Бабенко, Ю. В. Бабенко, Ю. В. For arbitrary t ∈ [0, 1], s ∈ [1, ∞], and A ≥ 2, we determine the unimprovable constant B for the inequality $$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$ . Для довільних t ∈ [0, 1], s ∈ [1, ∞] i A ≥ 2 знайдеио неполіпшувану константу В в нерівиості $$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$ . Institute of Mathematics, NAS of Ukraine 2001-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4239 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 2 (2001); 238-243 Український математичний журнал; Том 53 № 2 (2001); 238-243 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4239/5182 https://umj.imath.kiev.ua/index.php/umj/article/view/4239/5183 Copyright (c) 2001 Babenko Yu. V. |
| spellingShingle | Babenko, Yu. V. Бабенко, Ю. В. Бабенко, Ю. В. Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title | Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title_alt | Поточечные неравенства типа Ландау - Колмогорова для функций, заданных на конечном отрезке |
| title_full | Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title_fullStr | Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title_full_unstemmed | Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title_short | Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment |
| title_sort | pointwise inequalities of landau–kolmogorov type for functions defined on a finite segment |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4239 |
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