Boundedness of a class of multilinear operators and their iterated commutators on Morrey-Banach function spaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909489738809344 |
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| author | Tan, Jiawei Wang, Jiahui Xue, Qingying |
| author_facet | Tan, Jiawei Wang, Jiahui Xue, Qingying |
| contents | This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $ω$-Calderón-Zygmund operators, multilinear maximal singular integral operators, multilinear pseudo-differential operators, and multilinear square functions, as well as linear operators such as rough singular integral operators, nonintegral operators, and Stein's square functions. The boundedness of this class of operators and their commutators on Morrey-Banach spaces is established provided they satisfy either a pointwise sparse domination assumption or the $W_{r}$ property (Lerner, Lorist and Ombrosi, Math. Z. 2024), which significantly generalize the classical theory of Morrey spaces. As an application, the boundedness of iterated commutators of this class of multilinear operators is extended to Morrey-Lorentz spaces and Morrey spaces with variable exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundedness of a class of multilinear operators and their iterated commutators on Morrey-Banach function spaces Tan, Jiawei Wang, Jiahui Xue, Qingying Classical Analysis and ODEs 42B35 This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $ω$-Calderón-Zygmund operators, multilinear maximal singular integral operators, multilinear pseudo-differential operators, and multilinear square functions, as well as linear operators such as rough singular integral operators, nonintegral operators, and Stein's square functions. The boundedness of this class of operators and their commutators on Morrey-Banach spaces is established provided they satisfy either a pointwise sparse domination assumption or the $W_{r}$ property (Lerner, Lorist and Ombrosi, Math. Z. 2024), which significantly generalize the classical theory of Morrey spaces. As an application, the boundedness of iterated commutators of this class of multilinear operators is extended to Morrey-Lorentz spaces and Morrey spaces with variable exponents. |
| title | Boundedness of a class of multilinear operators and their iterated commutators on Morrey-Banach function spaces |
| topic | Classical Analysis and ODEs 42B35 |
| url | https://arxiv.org/abs/2502.08456 |