Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces
UDC 517.5 The higher-order commutators of  fractional Hardy-type operators  of variable order $\zeta(z)$ are shown to be bounded from the  grand variable  Herz spaces ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ into the weighted sp...
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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7546 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865794001419894784 |
|---|---|
| author | Sultan, Babar Sultan, Mehvish Sultan, Babar Sultan, Mehvish |
| author_facet | Sultan, Babar Sultan, Mehvish Sultan, Babar Sultan, Mehvish |
| author_institution_txt_mv | [
{
"author": "Babar Sultan",
"institution": "Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan"
},
{
"author": "Mehvish Sultan",
"institution": "Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan"
}
] |
| author_sort | Sultan, Babar |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-08-10T06:39:17Z |
| description | UDC 517.5
The higher-order commutators of  fractional Hardy-type operators  of variable order $\zeta(z)$ are shown to be bounded from the  grand variable  Herz spaces ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ into the weighted space ${\dot{K} ^{a(\cdot), u),\theta}_{\rho, q(\cdot)}(\mathbb{R}^n)},$ where $\rho=(1+|z_1|)^{-\lambda}$ and $\displaystyle {1 \over q(z)}={1 \over p(z)}-{\zeta (z) \over n}$ if $p(z)$ is not necessarily constant at infinity. |
| doi_str_mv | 10.3842/umzh.v76i7.7546 |
| first_indexed | 2026-03-24T03:32:41Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7546 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:41Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-75462024-08-10T06:39:17Z Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces Sultan, Babar Sultan, Mehvish Sultan, Babar Sultan, Mehvish exponent Lebesgue spaces BMO spaces weighted estimates Hardy operators grand Herz spaces Functional analysis operator theor UDC 517.5 The higher-order commutators of  fractional Hardy-type operators  of variable order $\zeta(z)$ are shown to be bounded from the  grand variable  Herz spaces ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ into the weighted space ${\dot{K} ^{a(\cdot), u),\theta}_{\rho, q(\cdot)}(\mathbb{R}^n)},$ where $\rho=(1+|z_1|)^{-\lambda}$ and $\displaystyle {1 \over q(z)}={1 \over p(z)}-{\zeta (z) \over n}$ if $p(z)$ is not necessarily constant at infinity. УДК 517.5 Теорема типу Соболєва для комутаторів операторів Гарді у великих просторах Герца  Показано, що комутатори вищих порядків дробових операторів типу Гарді змінного порядку $\zeta(z)$ обмежені з великих змінних просторів Герца ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ у ваговий простір ${\dot{K} ^{a(\cdot), u),\theta}_{\rho, q(\cdot)}(\mathbb{R}^n)},$ де $\rho=(1+|z_1|)^{-\lambda}$ і $\displaystyle {1 \over q(z)}={1 \over p(z)}-{\zeta (z) \over n}$, якщо $p(z)$ не обов'язково є сталою на нескінченності. Institute of Mathematics, NAS of Ukraine 2024-08-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7546 10.3842/umzh.v76i7.7546 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 7 (2024); 1052 - 1068 Український математичний журнал; Том 76 № 7 (2024); 1052 - 1068 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7546/10060 Copyright (c) 2024 Babar Sultan |
| spellingShingle | Sultan, Babar Sultan, Mehvish Sultan, Babar Sultan, Mehvish Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_alt | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_full | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_fullStr | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_full_unstemmed | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_short | Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces |
| title_sort | sobolev-type theorem for commutators of hardy operators in grand herz spaces |
| topic_facet | exponent Lebesgue spaces BMO spaces weighted estimates Hardy operators grand Herz spaces Functional analysis operator theor |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7546 |
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