Vector valued estimates for matrix weighted maximal operators and product $\mathrm{BMO}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912975548317696 |
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| author | Kakaroumpas, Spyridon Gibert, Odí Soler i |
| author_facet | Kakaroumpas, Spyridon Gibert, Odí Soler i |
| contents | We consider maximal operators acting on vector valued functions, that is, functions taking values on $\mathbb{C}^d,$ that incorporate matrix weights in their definitions. We show vector valued estimates, in the sense of Fefferman--Stein inequalities, for such operators. These are proven using an extrapolation result for convex body valued functions due to Bownik and Cruz-Uribe. Finally, we show an $\mathrm{H}^1$-$\mathrm{BMO}$ duality for matrix valued functions and we apply the previous vector valued estimates to show upper bounds for biparameter paraproducts. For the reader's convenience, we include an appendix explaining how to adapt the extrapolation for real convex body valued functions of Bownik and Cruz-Uribe to the setting of complex convex body valued functions that we treat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vector valued estimates for matrix weighted maximal operators and product $\mathrm{BMO}$ Kakaroumpas, Spyridon Gibert, Odí Soler i Functional Analysis Classical Analysis and ODEs 42B25, 42B30, 42B35 We consider maximal operators acting on vector valued functions, that is, functions taking values on $\mathbb{C}^d,$ that incorporate matrix weights in their definitions. We show vector valued estimates, in the sense of Fefferman--Stein inequalities, for such operators. These are proven using an extrapolation result for convex body valued functions due to Bownik and Cruz-Uribe. Finally, we show an $\mathrm{H}^1$-$\mathrm{BMO}$ duality for matrix valued functions and we apply the previous vector valued estimates to show upper bounds for biparameter paraproducts. For the reader's convenience, we include an appendix explaining how to adapt the extrapolation for real convex body valued functions of Bownik and Cruz-Uribe to the setting of complex convex body valued functions that we treat. |
| title | Vector valued estimates for matrix weighted maximal operators and product $\mathrm{BMO}$ |
| topic | Functional Analysis Classical Analysis and ODEs 42B25, 42B30, 42B35 |
| url | https://arxiv.org/abs/2407.16776 |