Sawyer estimates of mixed type for operators associated to a critical radius function
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910347460345856 |
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| author | Berra, Fabio Pradolini, Gladis Quijano, Pablo |
| author_facet | Berra, Fabio Pradolini, Gladis Quijano, Pablo |
| contents | We prove mixed inequalities for the Hardy-Littlewood maximal function $M^{ρ,σ}$, where $ρ$ is a critical radius function and $σ\geq 0$. We also exhibit and prove an extension of Cruz-Uribe, Martell and Pérez extrapolation result in \cite{CruzUribe-Martell-Perez} to the setting of Muckenhoupt weights associated to a critical radius function $ρ$. This theorem allows us to give mixed inequalities for Schrödinger-Calderón-Zygmund operators, extending some previous estimates that we have already proved in \cite{BPQ}. Since we are dealing with unrelated weights, the proof involves a quite subtle argument related with the original ideas from Sawyer in \cite{Sawyer}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sawyer estimates of mixed type for operators associated to a critical radius function Berra, Fabio Pradolini, Gladis Quijano, Pablo Classical Analysis and ODEs 42B20, 42B25, 35J10 We prove mixed inequalities for the Hardy-Littlewood maximal function $M^{ρ,σ}$, where $ρ$ is a critical radius function and $σ\geq 0$. We also exhibit and prove an extension of Cruz-Uribe, Martell and Pérez extrapolation result in \cite{CruzUribe-Martell-Perez} to the setting of Muckenhoupt weights associated to a critical radius function $ρ$. This theorem allows us to give mixed inequalities for Schrödinger-Calderón-Zygmund operators, extending some previous estimates that we have already proved in \cite{BPQ}. Since we are dealing with unrelated weights, the proof involves a quite subtle argument related with the original ideas from Sawyer in \cite{Sawyer}. |
| title | Sawyer estimates of mixed type for operators associated to a critical radius function |
| topic | Classical Analysis and ODEs 42B20, 42B25, 35J10 |
| url | https://arxiv.org/abs/2402.18504 |