Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces
In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha }^{p}$ with the symbols belong to the $p$-adic Lipschitz spaces in the context of the $p$-adic version of variable...
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Académie des sciences
2024-03-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.563/ |
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| author | Wu, Jianglong Chang, Yunpeng |
| author_facet | Wu, Jianglong Chang, Yunpeng |
| author_sort | Wu, Jianglong |
| collection | DOAJ |
| description | In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha }^{p}$ with the symbols belong to the $p$-adic Lipschitz spaces in the context of the $p$-adic version of variable Lebesgue spaces, by which some new characterizations of the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the $p$-adic field context. Meanwhile, Some equivalent relations between the $p$-adic Lipschitz norm and the $p$-adic variable Lebesgue norm are also given. |
| format | Article |
| id | doaj-art-a5a984cff877470e9835ed9babb58f32 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-a5a984cff877470e9835ed9babb58f322025-02-07T11:16:25ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-03-01362G217719410.5802/crmath.56310.5802/crmath.563Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue SpacesWu, Jianglong0Chang, Yunpeng1Department of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, ChinaDepartment of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, ChinaIn this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha }^{p}$ with the symbols belong to the $p$-adic Lipschitz spaces in the context of the $p$-adic version of variable Lebesgue spaces, by which some new characterizations of the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the $p$-adic field context. Meanwhile, Some equivalent relations between the $p$-adic Lipschitz norm and the $p$-adic variable Lebesgue norm are also given.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.563/$p$-adic fieldLipschitz functionfractional maximal functionvariable exponent Lebesgue space |
| spellingShingle | Wu, Jianglong Chang, Yunpeng Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces Comptes Rendus. Mathématique $p$-adic field Lipschitz function fractional maximal function variable exponent Lebesgue space |
| title | Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces |
| title_full | Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces |
| title_fullStr | Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces |
| title_full_unstemmed | Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces |
| title_short | Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces |
| title_sort | characterization of lipschitz spaces via commutators of fractional maximal function on the p adic variable exponent lebesgue spaces |
| topic | $p$-adic field Lipschitz function fractional maximal function variable exponent Lebesgue space |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.563/ |
| work_keys_str_mv | AT wujianglong characterizationoflipschitzspacesviacommutatorsoffractionalmaximalfunctiononthepadicvariableexponentlebesguespaces AT changyunpeng characterizationoflipschitzspacesviacommutatorsoffractionalmaximalfunctiononthepadicvariableexponentlebesguespaces |