Some estimates of multilinear operators on tent spaces
Let $ 0 < \alpha < mn $ and $ 0 < r, q < \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $ T_{r}^{q}(\mathbb{R}_{+}^{n+1}) $, where these multilinear operators includ...
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AIMS Press
2024-10-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024031 |
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| author | Heng Yang Jiang Zhou |
| author_facet | Heng Yang Jiang Zhou |
| author_sort | Heng Yang |
| collection | DOAJ |
| description | Let $ 0 < \alpha < mn $ and $ 0 < r, q < \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $ T_{r}^{q}(\mathbb{R}_{+}^{n+1}) $, where these multilinear operators include multilinear Hardy–Littlewood maximal operator $ \mathcal{M} $, multilinear fractional maximal operator $ \mathcal{M}_{\alpha} $, multilinear Calderón–Zygmund operator $ \mathcal{T} $, and multilinear fractional integral operator $ \mathcal{I}_{\alpha} $. Therefore, the results of Auscher and Prisuelos–Arribas [Math. Z. 286 (2017), 1575–1604] are extended to the general case. |
| format | Article |
| id | doaj-art-6c17479d2e8c4c3997e54f909118e044 |
| institution | Kabale University |
| issn | 2836-3310 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-6c17479d2e8c4c3997e54f909118e0442025-01-23T07:55:55ZengAIMS PressCommunications in Analysis and Mechanics2836-33102024-10-0116470071610.3934/cam.2024031Some estimates of multilinear operators on tent spacesHeng Yang0Jiang Zhou1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaLet $ 0 < \alpha < mn $ and $ 0 < r, q < \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $ T_{r}^{q}(\mathbb{R}_{+}^{n+1}) $, where these multilinear operators include multilinear Hardy–Littlewood maximal operator $ \mathcal{M} $, multilinear fractional maximal operator $ \mathcal{M}_{\alpha} $, multilinear Calderón–Zygmund operator $ \mathcal{T} $, and multilinear fractional integral operator $ \mathcal{I}_{\alpha} $. Therefore, the results of Auscher and Prisuelos–Arribas [Math. Z. 286 (2017), 1575–1604] are extended to the general case.https://www.aimspress.com/article/doi/10.3934/cam.2024031multilinear maximal operatormultilinear calderón–zygmund operatormultilinear fractional integral operatortent space |
| spellingShingle | Heng Yang Jiang Zhou Some estimates of multilinear operators on tent spaces Communications in Analysis and Mechanics multilinear maximal operator multilinear calderón–zygmund operator multilinear fractional integral operator tent space |
| title | Some estimates of multilinear operators on tent spaces |
| title_full | Some estimates of multilinear operators on tent spaces |
| title_fullStr | Some estimates of multilinear operators on tent spaces |
| title_full_unstemmed | Some estimates of multilinear operators on tent spaces |
| title_short | Some estimates of multilinear operators on tent spaces |
| title_sort | some estimates of multilinear operators on tent spaces |
| topic | multilinear maximal operator multilinear calderón–zygmund operator multilinear fractional integral operator tent space |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2024031 |
| work_keys_str_mv | AT hengyang someestimatesofmultilinearoperatorsontentspaces AT jiangzhou someestimatesofmultilinearoperatorsontentspaces |