On pointwise convergence of multilinear Bochner-Riesz means
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909410299740160 |
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| author | He, Danqing Li, Kangwei Zheng, Jiqiang |
| author_facet | He, Danqing Li, Kangwei Zheng, Jiqiang |
| contents | We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively, which is new when $p<2/k$ in higher dimensions. To prove these estimates, we make use of a variant of Stein's square function and its multilinear generalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On pointwise convergence of multilinear Bochner-Riesz means He, Danqing Li, Kangwei Zheng, Jiqiang Classical Analysis and ODEs We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively, which is new when $p<2/k$ in higher dimensions. To prove these estimates, we make use of a variant of Stein's square function and its multilinear generalization. |
| title | On pointwise convergence of multilinear Bochner-Riesz means |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2412.00296 |