Maximal operator on variable exponent spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915152547282944 |
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| author | Adamadze, Daviti Diening, Lars Kopaliani, Tengiz |
| author_facet | Adamadze, Daviti Diening, Lars Kopaliani, Tengiz |
| contents | We explore the boundedness of the Hardy-Littlewood maximal operator $M$ on variable exponent spaces. Our findings demonstrate that the Muckenhoupt condition, in conjunction with Nekvinda's decay condition, implies the boundedness of $M$ even for unbounded exponents. This extends the results of Lerner, Cruz-Uribe and Fiorenza for bounded exponents. We also introduce a novel argument that allows approximate unbounded exponents by bounded ones while preserving the Muckenhoupt and Nekvinda conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal operator on variable exponent spaces Adamadze, Daviti Diening, Lars Kopaliani, Tengiz Functional Analysis 42B25, 46E30 We explore the boundedness of the Hardy-Littlewood maximal operator $M$ on variable exponent spaces. Our findings demonstrate that the Muckenhoupt condition, in conjunction with Nekvinda's decay condition, implies the boundedness of $M$ even for unbounded exponents. This extends the results of Lerner, Cruz-Uribe and Fiorenza for bounded exponents. We also introduce a novel argument that allows approximate unbounded exponents by bounded ones while preserving the Muckenhoupt and Nekvinda conditions. |
| title | Maximal operator on variable exponent spaces |
| topic | Functional Analysis 42B25, 46E30 |
| url | https://arxiv.org/abs/2502.10313 |