Bochner-Riesz means at the critical index: Weighted and sparse bounds
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912200116928512 |
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| author | Beltran, David Roos, Joris Seeger, Andreas |
| author_facet | Beltran, David Roos, Joris Seeger, Andreas |
| contents | We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $λ(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension $d=2$; partial results as well as conditional results are proved in higher dimensions. For the means of index $λ_*=\frac{d-1}{2d+2}$ we prove fully optimal sparse bounds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_13487 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bochner-Riesz means at the critical index: Weighted and sparse bounds Beltran, David Roos, Joris Seeger, Andreas Classical Analysis and ODEs 42B15, 42B20, 42B25 We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $λ(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension $d=2$; partial results as well as conditional results are proved in higher dimensions. For the means of index $λ_*=\frac{d-1}{2d+2}$ we prove fully optimal sparse bounds. |
| title | Bochner-Riesz means at the critical index: Weighted and sparse bounds |
| topic | Classical Analysis and ODEs 42B15, 42B20, 42B25 |
| url | https://arxiv.org/abs/2309.13487 |