Two-weight extrapolation on function spaces and applications
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909299804995584 |
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| author | Cao, Mingming Olivo, Andrea |
| author_facet | Cao, Mingming Olivo, Andrea |
| contents | This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including $A_1$, $A_p$, and $A_\infty$ extrapolation in the context of Banach function spaces, and also on modular spaces. We also include several applications that can be easily obtained using extrapolation: local decay estimates for various operators, Coifman--Fefferman inequalities that can be used to show some known sharp $A_1$ inequalities, Muckenhoupt--Wheeden and Sawyer's conjectures are also presented for many operators, which go beyond Calderón--Zygmund operators. Finally, we obtain two-weight inequalities for Littlewood--Paley operators and Fourier integral operators on weighted Banach function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06920 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Two-weight extrapolation on function spaces and applications Cao, Mingming Olivo, Andrea Classical Analysis and ODEs Functional Analysis 42B20, 42B25, 42B35, 46E30 This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including $A_1$, $A_p$, and $A_\infty$ extrapolation in the context of Banach function spaces, and also on modular spaces. We also include several applications that can be easily obtained using extrapolation: local decay estimates for various operators, Coifman--Fefferman inequalities that can be used to show some known sharp $A_1$ inequalities, Muckenhoupt--Wheeden and Sawyer's conjectures are also presented for many operators, which go beyond Calderón--Zygmund operators. Finally, we obtain two-weight inequalities for Littlewood--Paley operators and Fourier integral operators on weighted Banach function spaces. |
| title | Two-weight extrapolation on function spaces and applications |
| topic | Classical Analysis and ODEs Functional Analysis 42B20, 42B25, 42B35, 46E30 |
| url | https://arxiv.org/abs/2101.06920 |