Sharp weighted non-tangential maximal estimates via Carleson-sparse domination
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913490070929408 |
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| author | Rosén, Andreas |
| author_facet | Rosén, Andreas |
| contents | We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from $\mathbf{R}^n$ to the half-space in $\mathbf{R}^{1+n}$ above $\mathbf{R}^n$. The proof is based on pointwise sparse domination of the adjoint singular integrals that map functions from the half-space back to the boundary. It is proved that these map $L_1$ functions in the half-space to weak $L_1$ functions on the boundary. From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp weighted non-tangential maximal estimates via Carleson-sparse domination Rosén, Andreas Classical Analysis and ODEs 42B35, 42B20, 42B37 We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from $\mathbf{R}^n$ to the half-space in $\mathbf{R}^{1+n}$ above $\mathbf{R}^n$. The proof is based on pointwise sparse domination of the adjoint singular integrals that map functions from the half-space back to the boundary. It is proved that these map $L_1$ functions in the half-space to weak $L_1$ functions on the boundary. From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages. |
| title | Sharp weighted non-tangential maximal estimates via Carleson-sparse domination |
| topic | Classical Analysis and ODEs 42B35, 42B20, 42B37 |
| url | https://arxiv.org/abs/2406.01776 |