Abstract:We consider vector-valued magnetic Schrödinger operators $-\bm \Delta_{\bm a}+V$ with magnetic potential $\bm a \in L^2_{\mathrm{loc}}(\mathbb{R}^d;\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\mathrm{loc}}(\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\mathbb{R}^d;\mathbb{C}^m)$, $p\in[1,\infty)$ and the boundedness of the Riesz transforms $(\nabla - i\bm a)(-\bm \Delta_{\bm a}+V)^{-\frac{1}{2}}$ and $V^{\alpha}(-\bm \Delta_{\bm a}+V)^{-\alpha}$ on $L^p(\mathbb{R}^d;\mathbb{C}^m)$ for every $p \in (1,2]$ and every $\alpha\in[0,1/p]$.
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 35J47, 47D08, 42B20, 42B37 |
| Cite as: | arXiv:2605.19438 [math.AP] |
| (or arXiv:2605.19438v2 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.19438 arXiv-issued DOI via DataCite |
From: Luca Lorenzi [view email]
[v1]
Tue, 19 May 2026 06:48:37 UTC (37 KB)
[v2]
Fri, 22 May 2026 05:47:29 UTC (37 KB)
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