Some estimates for commutators of the fractional maximal function on stratified Lie groups
Abstract In this paper, the main aim is to consider the boundedness of the nonlinear commutator [ b , M α ] $[b, M_{\alpha}]$ and the maximal commutator M α , b $M_{\alpha ,b}$ on the Lebesgue spaces over some stratified Lie group G $\mathbb{G}$ when the symbol b belongs to the Lipschitz space. As a...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-09-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03037-6 |
| _version_ | 1797555720504213504 |
|---|---|
| author | Jianglong Wu Wenjiao Zhao |
| author_facet | Jianglong Wu Wenjiao Zhao |
| author_sort | Jianglong Wu |
| collection | DOAJ |
| description | Abstract In this paper, the main aim is to consider the boundedness of the nonlinear commutator [ b , M α ] $[b, M_{\alpha}]$ and the maximal commutator M α , b $M_{\alpha ,b}$ on the Lebesgue spaces over some stratified Lie group G $\mathbb{G}$ when the symbol b belongs to the Lipschitz space. As a result, some new characterizations of the Lipschitz spaces on Lie group via [ b , M α ] $[b, M_{\alpha}]$ and M α , b $M_{\alpha ,b}$ are given. |
| first_indexed | 2024-03-10T16:51:29Z |
| format | Article |
| id | doaj.art-19b06627c0ee4546bbed441687ea2d7d |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-10T16:51:29Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-19b06627c0ee4546bbed441687ea2d7d2023-11-20T11:16:20ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-09-012023111710.1186/s13660-023-03037-6Some estimates for commutators of the fractional maximal function on stratified Lie groupsJianglong Wu0Wenjiao Zhao1Department of Mathematics, Mudanjiang Normal UniversitySchool of Mathematics, Physics and Finance, Anhui Polytechnic UniversityAbstract In this paper, the main aim is to consider the boundedness of the nonlinear commutator [ b , M α ] $[b, M_{\alpha}]$ and the maximal commutator M α , b $M_{\alpha ,b}$ on the Lebesgue spaces over some stratified Lie group G $\mathbb{G}$ when the symbol b belongs to the Lipschitz space. As a result, some new characterizations of the Lipschitz spaces on Lie group via [ b , M α ] $[b, M_{\alpha}]$ and M α , b $M_{\alpha ,b}$ are given.https://doi.org/10.1186/s13660-023-03037-6Stratified Lie groupFractional maximal functionLipschitz functionCommutator |
| spellingShingle | Jianglong Wu Wenjiao Zhao Some estimates for commutators of the fractional maximal function on stratified Lie groups Journal of Inequalities and Applications Stratified Lie group Fractional maximal function Lipschitz function Commutator |
| title | Some estimates for commutators of the fractional maximal function on stratified Lie groups |
| title_full | Some estimates for commutators of the fractional maximal function on stratified Lie groups |
| title_fullStr | Some estimates for commutators of the fractional maximal function on stratified Lie groups |
| title_full_unstemmed | Some estimates for commutators of the fractional maximal function on stratified Lie groups |
| title_short | Some estimates for commutators of the fractional maximal function on stratified Lie groups |
| title_sort | some estimates for commutators of the fractional maximal function on stratified lie groups |
| topic | Stratified Lie group Fractional maximal function Lipschitz function Commutator |
| url | https://doi.org/10.1186/s13660-023-03037-6 |
| work_keys_str_mv | AT jianglongwu someestimatesforcommutatorsofthefractionalmaximalfunctiononstratifiedliegroups AT wenjiaozhao someestimatesforcommutatorsofthefractionalmaximalfunctiononstratifiedliegroups |