A modulus of smoothness for some Banach function spaces
UDC 517.5 Based on the Steklov operator, we consider a modulus of smoothness of functions in some Banach function spaces, which can be not translation invariant and establish its main properties.  A constructive characterization of the Lipschitz class is obtained by using the Jackson-ty...
Gespeichert in:
| Datum: | 2023 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/970 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507231028510720 |
|---|---|
| author | Akgün, Ramazan Akgün, Ramazan |
| author_facet | Akgün, Ramazan Akgün, Ramazan |
| author_sort | Akgün, Ramazan |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:34:31Z |
| description | UDC 517.5
Based on the Steklov operator, we consider a modulus of smoothness of functions in some Banach function spaces, which can be not translation invariant and establish its main properties.  A constructive characterization of the Lipschitz class is obtained by using the Jackson-type direct theorem and inverse theorem of trigonometric approximation. As application, we present several examples of related (weighted) function spaces. |
| doi_str_mv | 10.3842/umzh.v75i8.970 |
| first_indexed | 2026-03-24T02:06:00Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-970 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:06:00Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-9702024-06-19T00:34:31Z A modulus of smoothness for some Banach function spaces A modulus of smoothness for some Banach function spaces Akgün, Ramazan Akgün, Ramazan A constructive characterization UDC 517.5 Based on the Steklov operator, we consider a modulus of smoothness of functions in some Banach function spaces, which can be not translation invariant and establish its main properties.  A constructive characterization of the Lipschitz class is obtained by using the Jackson-type direct theorem and inverse theorem of trigonometric approximation. As application, we present several examples of related (weighted) function spaces. УДК 517.5 Модуль гладкості для деяких банахових функціональних просторів На основі оператора Стєклова розглянуто модуль гладкості функцій у деяких банахових функціональних просторах, які можуть не бути трансляційно-інваріантними, та вивчено його основні властивості. Конструктивну характеристику класу Ліпшиця отримано за допомогою прямої теореми типу Джексона та оберненої теореми про тригонометричне наближення. Як застосування, наведено кілька прикладів відповідних (вагових) функціональних просторів. Institute of Mathematics, NAS of Ukraine 2023-08-30 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/970 10.3842/umzh.v75i8.970 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 8 (2023); 1015 - 1031 Український математичний журнал; Том 75 № 8 (2023); 1015 - 1031 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/970/9737 Copyright (c) 2023 Ramazan AKGÜN |
| spellingShingle | Akgün, Ramazan Akgün, Ramazan A modulus of smoothness for some Banach function spaces |
| title | A modulus of smoothness for some Banach function spaces |
| title_alt | A modulus of smoothness for some Banach function spaces |
| title_full | A modulus of smoothness for some Banach function spaces |
| title_fullStr | A modulus of smoothness for some Banach function spaces |
| title_full_unstemmed | A modulus of smoothness for some Banach function spaces |
| title_short | A modulus of smoothness for some Banach function spaces |
| title_sort | modulus of smoothness for some banach function spaces |
| topic_facet | A constructive characterization |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/970 |
| work_keys_str_mv | AT akgunramazan amodulusofsmoothnessforsomebanachfunctionspaces AT akgunramazan amodulusofsmoothnessforsomebanachfunctionspaces AT akgunramazan modulusofsmoothnessforsomebanachfunctionspaces AT akgunramazan modulusofsmoothnessforsomebanachfunctionspaces |