Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class
UDC 517.5 We prove some relations between the discrete Gehring classes $\mathcal{G}_{q}$ and the discrete Muckenhoupt classes  $\mathcal{A}_{p}.$  Specifically, by using some known Hardy-type and Carleman-type inequalities...
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| Datum: | 2023 |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6788 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512513308753920 |
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| author | Saker, S. H. Mahmoud, R. R. Hassan, M. H. Saker, S. H. Mahmoud, R. R. Hassan, M. H. |
| author_facet | Saker, S. H. Mahmoud, R. R. Hassan, M. H. Saker, S. H. Mahmoud, R. R. Hassan, M. H. |
| author_sort | Saker, S. H. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-04-14T15:06:07Z |
| description | UDC 517.5
We prove some relations between the discrete Gehring classes $\mathcal{G}_{q}$ and the discrete Muckenhoupt classes  $\mathcal{A}_{p}.$  Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between $\mathcal{G}_{1},$ $\mathcal{A}_{\infty }$ and $\mathcal{A}_{1}$ for nonincreasing and nondecreasing weights.  Finally, we establish some general results by introducing the notions of $\mathcal{G}_{\varphi }$ classes defined for nonnegative convex function $\varphi.$ |
| doi_str_mv | 10.37863/umzh.v75i3.6788 |
| first_indexed | 2026-03-24T03:29:59Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6788 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:59Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67882023-04-14T15:06:07Z Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class Saker, S. H. Mahmoud, R. R. Hassan, M. H. Saker, S. H. Mahmoud, R. R. Hassan, M. H. Gehring class, Muckenhoupt class, Hardy inequality, Carleman inequality. 42B25, 26D15, 42B35. UDC 517.5 We prove some relations between the discrete Gehring classes $\mathcal{G}_{q}$ and the discrete Muckenhoupt classes  $\mathcal{A}_{p}.$  Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between $\mathcal{G}_{1},$ $\mathcal{A}_{\infty }$ and $\mathcal{A}_{1}$ for nonincreasing and nondecreasing weights.  Finally, we establish some general results by introducing the notions of $\mathcal{G}_{\varphi }$ classes defined for nonnegative convex function $\varphi.$ УДК 517.5 Кількісна залежність деяких дискретних граничних класів від класу Макенхаупта ${\cal A}_1(u)$ Доведено деякі співвідношення між дискретними класами Герінга $\mathcal{G}_{q}$ і дискретними класами Макенхаупта  $\mathcal{A}_{p}.$  Зокрема, застосовуючи деякі відомі  нерівності типу Гарді та Карлемана,  вивчeно зв’язок між $\mathcal{G}_{1},$ $\mathcal{A}_{\infty }$ і $\mathcal{A}_{1}$ для незростаючих та неспадаючих ваг.  Крім того, встановлено деякі загальні результати на підставі введеного  поняття класів $\mathcal{G}_{\varphi }$, що визначені для невід’ємної опуклої функції $\varphi.$ Institute of Mathematics, NAS of Ukraine 2023-04-11 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6788 10.37863/umzh.v75i3.6788 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 3 (2023); 397 - 415 Український математичний журнал; Том 75 № 3 (2023); 397 - 415 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6788/9791 Copyright (c) 2023 Ramy Mahmoud |
| spellingShingle | Saker, S. H. Mahmoud, R. R. Hassan, M. H. Saker, S. H. Mahmoud, R. R. Hassan, M. H. Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_alt | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_full | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_fullStr | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_full_unstemmed | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_short | Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class |
| title_sort | quantitative dependence of some discrete limiting classes on the muckenhoupt ${\cal a}_1(u)$ class |
| topic_facet | Gehring class Muckenhoupt class Hardy inequality Carleman inequality. 42B25 26D15 42B35. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6788 |
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