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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02607 |
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| _version_ | 1866910435012247552 |
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| author | Chen, Peng He, Danqing Li, Xiaochun Yan, Lixin |
| author_facet | Chen, Peng He, Danqing Li, Xiaochun Yan, Lixin |
| contents | For $p\ge 2$, and $λ>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^λ(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\ \widehat f\subset\{ξ\in\mathbb R^n:\ 1<|ξ_n|<2\}$. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On pointwise convergence of cone multipliers Chen, Peng He, Danqing Li, Xiaochun Yan, Lixin Classical Analysis and ODEs For $p\ge 2$, and $λ>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^λ(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\ \widehat f\subset\{ξ\in\mathbb R^n:\ 1<|ξ_n|<2\}$. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones. |
| title | On pointwise convergence of cone multipliers |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2405.02607 |