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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.04082 |
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| _version_ | 1866914075983740928 |
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| author | Guo, Huanqing Zhang, Junyong Zheng, Jiqiang |
| author_facet | Guo, Huanqing Zhang, Junyong Zheng, Jiqiang |
| contents | This paper studies the sharp $L^p$-$L^q$ boundedness of the Bochner-Riesz operator $S^δ_λ(\mathcal{L}_{\mathbf{A}})$ associated with a scaling-critical magnetic Schrödinger operator $\mathcal{L}_{\mathbf{A}}$ on $\mathbb{R}^2$, where $δ\in (-3/2, 0)$. We determine the conditions on the exponents $p$ and $q$ under which the operator is bounded from $L^p(\mathbb{R}^2)$ to $L^q(\mathbb{R}^2)$. Our main result characterizes the boundedness region as a pentagonal subset $Δ(δ)$ of the $(1/p, 1/q)$-plane, extending previous uniform resolvent result in Fanelli, Zhang and Zheng[Int. Math. Res. Not., 20(2023), 17656-17703]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $\mathbb{R}^2$ Guo, Huanqing Zhang, Junyong Zheng, Jiqiang Analysis of PDEs This paper studies the sharp $L^p$-$L^q$ boundedness of the Bochner-Riesz operator $S^δ_λ(\mathcal{L}_{\mathbf{A}})$ associated with a scaling-critical magnetic Schrödinger operator $\mathcal{L}_{\mathbf{A}}$ on $\mathbb{R}^2$, where $δ\in (-3/2, 0)$. We determine the conditions on the exponents $p$ and $q$ under which the operator is bounded from $L^p(\mathbb{R}^2)$ to $L^q(\mathbb{R}^2)$. Our main result characterizes the boundedness region as a pentagonal subset $Δ(δ)$ of the $(1/p, 1/q)$-plane, extending previous uniform resolvent result in Fanelli, Zhang and Zheng[Int. Math. Res. Not., 20(2023), 17656-17703]. |
| title | Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $\mathbb{R}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04082 |