New fractional type weights and the boundedness of some operators
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916605034758144 |
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| author | Cen, Xi He, Qianjun Song, Zichen Wang, Zihan |
| author_facet | Cen, Xi He, Qianjun Song, Zichen Wang, Zihan |
| contents | Two classes of fractional type variable weights are established in this paper. The first kind of weights ${A_{\vec p( \cdot ),q( \cdot )}}$ are variable multiple weights, which are characterized by the weighted variable boundedness of multilinear fractional type operators, called multilinear Hardy--Littlewood--Sobolev theorem on weighted variable Lebesgue spaces. Meanwhile, the weighted variable boundedness for the commutators of multilinear fractional type operators are also obtained. This generalizes some known work, such as Moen (2009), Bernardis--Dalmasso--Pradolini (2014), and Cruz-Uribe--Guzmán (2020). Another class of weights ${\mathbb{A}_{p( \cdot ),q(\cdot)}}$ are variable matrix weights that also characterized by certain fractional type operators. This generalize some previous results on matrix weights ${\mathbb{A}_{p( \cdot )}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New fractional type weights and the boundedness of some operators Cen, Xi He, Qianjun Song, Zichen Wang, Zihan Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B20, 42B25, 42B35 Two classes of fractional type variable weights are established in this paper. The first kind of weights ${A_{\vec p( \cdot ),q( \cdot )}}$ are variable multiple weights, which are characterized by the weighted variable boundedness of multilinear fractional type operators, called multilinear Hardy--Littlewood--Sobolev theorem on weighted variable Lebesgue spaces. Meanwhile, the weighted variable boundedness for the commutators of multilinear fractional type operators are also obtained. This generalizes some known work, such as Moen (2009), Bernardis--Dalmasso--Pradolini (2014), and Cruz-Uribe--Guzmán (2020). Another class of weights ${\mathbb{A}_{p( \cdot ),q(\cdot)}}$ are variable matrix weights that also characterized by certain fractional type operators. This generalize some previous results on matrix weights ${\mathbb{A}_{p( \cdot )}}$. |
| title | New fractional type weights and the boundedness of some operators |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B20, 42B25, 42B35 |
| url | https://arxiv.org/abs/2310.10470 |