Weighted Lorentz spaces: sharp mixed $A_p-A_{\infty}$ estimate for maximal functions
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910627679698944 |
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| author | Accomazzo, Natalia Duoandikoetxea, Javier Nieraeth, Zoe Ombrosi, Sheldy Pérez, Carlos |
| author_facet | Accomazzo, Natalia Duoandikoetxea, Javier Nieraeth, Zoe Ombrosi, Sheldy Pérez, Carlos |
| contents | We prove the sharp mixed $A_{p}-A_{\infty}$ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely \[ \|M\|_{L^{p,q}(w)} \lesssim_{p,q,n} [w]^{\frac1p}_{A_p}[σ]^{\frac1{\min(p,q)}}_{A_{\infty}}, \] where $σ=w^{\frac{1}{1-p}}$. Our method is rearrangement free and can also be used to bound similar operators, even in the two-weight setting. We use this to also obtain new quantitative bounds for the strong maximal operator and for $M$ in a dual setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12692 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Weighted Lorentz spaces: sharp mixed $A_p-A_{\infty}$ estimate for maximal functions Accomazzo, Natalia Duoandikoetxea, Javier Nieraeth, Zoe Ombrosi, Sheldy Pérez, Carlos Classical Analysis and ODEs Functional Analysis Primary: 42B25. Secondary: 42B20 We prove the sharp mixed $A_{p}-A_{\infty}$ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely \[ \|M\|_{L^{p,q}(w)} \lesssim_{p,q,n} [w]^{\frac1p}_{A_p}[σ]^{\frac1{\min(p,q)}}_{A_{\infty}}, \] where $σ=w^{\frac{1}{1-p}}$. Our method is rearrangement free and can also be used to bound similar operators, even in the two-weight setting. We use this to also obtain new quantitative bounds for the strong maximal operator and for $M$ in a dual setting. |
| title | Weighted Lorentz spaces: sharp mixed $A_p-A_{\infty}$ estimate for maximal functions |
| topic | Classical Analysis and ODEs Functional Analysis Primary: 42B25. Secondary: 42B20 |
| url | https://arxiv.org/abs/2111.12692 |